One-Dimensional Ising Model with "k"-Spin Interactions
ERIC Educational Resources Information Center
Fan, Yale
2011-01-01
We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…
Bootstrapping Critical Ising Model on Three Dimensional Real Projective Space.
Nakayama, Yu
2016-04-01
Given conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three dimensional real projective space. We check the rapid convergence of our bootstrap program in two dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three dimensional real projective space is less than 1%. Our method opens up a novel way to solve conformal field theories on nontrivial geometries. PMID:27104697
Bootstrapping Critical Ising Model on Three Dimensional Real Projective Space
NASA Astrophysics Data System (ADS)
Nakayama, Yu
2016-04-01
Given conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three dimensional real projective space. We check the rapid convergence of our bootstrap program in two dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three dimensional real projective space is less than 1%. Our method opens up a novel way to solve conformal field theories on nontrivial geometries.
One-dimensional Ising model with multispin interactions
NASA Astrophysics Data System (ADS)
Turban, Loïc
2016-09-01
We study the spin-1/2 Ising chain with multispin interactions K involving the product of m successive spins, for general values of m. Using a change of spin variables the zero-field partition function of a finite chain is obtained for free and periodic boundary conditions and we calculate the two-spin correlation function. When placed in an external field H the system is shown to be self-dual. Using another change of spin variables the one-dimensional Ising model with multispin interactions in a field is mapped onto a zero-field rectangular Ising model with first-neighbour interactions K and H. The 2D system, with size m × N/m, has the topology of a cylinder with helical BC. In the thermodynamic limit N/m\\to ∞ , m\\to ∞ , a 2D critical singularity develops on the self-duality line, \\sinh 2K\\sinh 2H=1.
Thermodynamics of trajectories of the one-dimensional Ising model
NASA Astrophysics Data System (ADS)
Loscar, Ernesto S.; Mey, Antonia S. J. S.; Garrahan, Juan P.
2011-12-01
We present a numerical study of the dynamics of the one-dimensional Ising model by applying the large-deviation method to describe ensembles of dynamical trajectories. In this approach trajectories are classified according to a dynamical order parameter and the structure of ensembles of trajectories can be understood from the properties of large-deviation functions, which play the role of dynamical free-energies. We consider both Glauber and Kawasaki dynamics, and also the presence of a magnetic field. For Glauber dynamics in the absence of a field we confirm the analytic predictions of Jack and Sollich about the existence of critical dynamical, or space-time, phase transitions at critical values of the 'counting' field s. In the presence of a magnetic field the dynamical phase diagram also displays first order transition surfaces. We discuss how these non-equilibrium transitions in the 1d Ising model relate to the equilibrium ones of the 2d Ising model. For Kawasaki dynamics we find a much simpler dynamical phase structure, with transitions reminiscent of those seen in kinetically constrained models.
Information theoretic aspects of the two-dimensional Ising model.
Lau, Hon Wai; Grassberger, Peter
2013-02-01
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference 2H(L)(w)-H(2L)(w) between entropies on cylinders of finite lengths L and 2L with open end cap boundaries, in the limit L→∞. This essentially quantifies how the finite length correction for the entropy scales with the cylinder circumference w. Secondly, using the transfer matrix, we obtain precise estimates for the information needed to specify the spin state on a ring encircling an infinitely long cylinder. Combining both results, we obtain the mutual information between the two halves of a cylinder (the "excess entropy" for the cylinder), where we confirm with higher precision but for smaller systems the results recently obtained by Wilms et al., and we show that the mutual information between the two halves of the ring diverges at the critical point logarithmically with w. Finally, we use the second result together with Monte Carlo simulations to show that also the excess entropy of a straight line of n spins in an infinite lattice diverges at criticality logarithmically with n. We conjecture that such logarithmic divergence happens generically for any one-dimensional subset of sites at any two-dimensional second-order phase transition. Comparing straight lines on square and triangular lattices with square loops and with lines of thickness 2, we discuss questions of universality. PMID:23496480
Information theoretic aspects of the two-dimensional Ising model
NASA Astrophysics Data System (ADS)
Lau, Hon Wai; Grassberger, Peter
2013-02-01
We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference 2HL(w)-H2L(w) between entropies on cylinders of finite lengths L and 2L with open end cap boundaries, in the limit L→∞. This essentially quantifies how the finite length correction for the entropy scales with the cylinder circumference w. Secondly, using the transfer matrix, we obtain precise estimates for the information needed to specify the spin state on a ring encircling an infinitely long cylinder. Combining both results, we obtain the mutual information between the two halves of a cylinder (the “excess entropy” for the cylinder), where we confirm with higher precision but for smaller systems the results recently obtained by Wilms , and we show that the mutual information between the two halves of the ring diverges at the critical point logarithmically with w. Finally, we use the second result together with Monte Carlo simulations to show that also the excess entropy of a straight line of n spins in an infinite lattice diverges at criticality logarithmically with n. We conjecture that such logarithmic divergence happens generically for any one-dimensional subset of sites at any two-dimensional second-order phase transition. Comparing straight lines on square and triangular lattices with square loops and with lines of thickness 2, we discuss questions of universality.
Algorithmic proof for the completeness of the two-dimensional Ising model
NASA Astrophysics Data System (ADS)
Karimipour, Vahid; Zarei, Mohammad Hossein
2012-11-01
We show that the two-dimensional (2D) Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all its spin-spin coupling equal to i(π)/(4) and all parameters of the original model are contained in the local magnetic fields of the Ising model. This result has already been derived by using techniques from quantum information theory and by exploiting the universality of cluster states. Here we do not use the quantum formalism and hence make the completeness result accessible to a wide audience. Furthermore, our method has the advantage of being algorithmic in nature so that, by following a set of simple graphical transformations, one is able to transform any discrete lattice model to an Ising model defined on a (polynomially) larger 2D lattice.
Mathematical structure of the three-dimensional (3D) Ising model
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Dong
2013-03-01
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given from the points of view of topology, algebra, and geometry. By analyzing the relationships among transfer matrices of the 3D Ising model, Reidemeister moves in the knot theory, Yang-Baxter and tetrahedron equations, the following facts are illustrated for the 3D Ising model. 1) The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a (3+1)-dimensional space-time as a relativistic quantum statistical mechanics model, which is consistent with the 4-fold integrand of the partition function obtained by taking the time average. 2) A unitary transformation with a matrix that is a spin representation in 2n·l·o-space corresponds to a rotation in 2n·l·o-space, which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model. 3) A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model, and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures. 4) The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases varphix, varphiy, and varphiz. The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail. The conjectured exact solution is compared with numerical results, and the singularities at/near infinite temperature are inspected. The analyticity in β = 1/(kBT) of both the hard-core and the Ising models has been proved only for β > 0, not for β = 0. Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.
Linear relaxation in large two-dimensional Ising models
NASA Astrophysics Data System (ADS)
Lin, Y.; Wang, F.
2016-02-01
Critical dynamics in two-dimension Ising lattices up to 2048 ×2048 is simulated on field-programmable-gate-array- based computing devices. Linear relaxation times are measured from extremely long Monte Carlo simulations. The longest simulation has 7.1 ×1016 spin updates, which would take over 37 years to simulate on a general purpose computer. The linear relaxation time of the Ising lattices is found to follow the dynamic scaling law for correlation lengths as long as 2048. The dynamic exponent z of the system is found to be 2.179(12), which is consistent with previous studies of Ising lattices with shorter correlation lengths. It is also found that Monte Carlo simulations of critical dynamics in Ising lattices larger than 512 ×512 are very sensitive to the statistical correlations between pseudorandom numbers, making it even more difficult to study such large systems.
One-dimensional random field Ising model and discrete stochastic mappings
Behn, U.; Zagrebnov, V.A.
1987-06-01
Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.
Phase diagram of the three-dimensional axial next-nearest-neighbor Ising model
NASA Astrophysics Data System (ADS)
Gendiar, A.; Nishino, T.
2005-01-01
The three-dimensional axial next-nearest-neighbor Ising model is studied by a modified tensor product variational approach. A global phase diagram is constructed with numerous commensurate and incommensurate magnetic phases. The devil’s stairs behavior for the model is confirmed. The wavelength of the spin modulated phases increases to infinity at the boundary with the ferromagnetic phase. Widths of the commensurate phases are considerably narrower than those calculated by mean-field approximations.
NASA Astrophysics Data System (ADS)
Merdan, Ziya; Karakuş, Özlem
2016-07-01
The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.
Finite-size scaling and the three-dimensional Ising model
NASA Astrophysics Data System (ADS)
Bhanot, G.; Duke, D.; Salvador, R.
1986-06-01
We give results of an extensive finite-size-scaling analysis of the three-dimensional Ising model on lattices of size up to 443. Contrary to the results of Barber et al.
Statics and Dynamics of a Two-Dimensional Ising Spin-Glass Model
NASA Astrophysics Data System (ADS)
Young, A. P.
1983-03-01
The temperature and field dependence of spatial correlations and relaxation times are investigated in detail by Monte Carlo simulations for a two-dimensional Ising spin-glass model. There is no transition, but, in zero field, barrier heights and correlation range increase smoothly at low temperatures. This increase does not seem to be fast enough to explain experiments. In a field, barrier heights and the correlation length tend to a finite limit as T-->0. Points in the h-T plane with constant relaxation time satisfy T(h)-T(0)~h23 at moderately low temperatures.
Two-dimensional XXZ -Ising model on a square-hexagon lattice
NASA Astrophysics Data System (ADS)
Valverde, J. S.; Rojas, Onofre; de Souza, S. M.
2009-04-01
We study a two-dimensional XXZ -Ising model on a square-hexagon (denoted for simplicity by 4-6) lattice with spin 1/2. The phase diagram at zero temperature is discussed, where five states are found, two types of ferrimagnetic states, two types of antiferromagnetic states, and one ferromagnetic state. To solve this model, we have mapped onto the eight-vertex model with union Jack interaction term, and it was verified that the model cannot be completely mapped onto eight-vertex model. However, by imposing an exact solution condition, we have found the region where the XXZ -Ising model on 4-6 lattice is exactly soluble with one free parameter, particularly for the case of symmetric eight-vertex model condition. In this manner we have explored the properties of the system and have analyzed the interacting competition parameters which preserve the region where there is an exact solution. Unfortunately the present model does not satisfy the free fermion condition of the eight-vertex model, unless for a trivial solution. Even so, we are able to discuss the critical point region, beyond the region of exact resolvability.
Flocking with discrete symmetry: The two-dimensional active Ising model
NASA Astrophysics Data System (ADS)
Solon, A. P.; Tailleur, J.
2015-10-01
We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.
Critical behavior of the two-dimensional Ising model with long-range correlated disorder
NASA Astrophysics Data System (ADS)
Dudka, M.; Fedorenko, A. A.; Blavatska, V.; Holovatch, Yu.
2016-06-01
We study critical behavior of the diluted two-dimensional Ising model in the presence of disorder correlations which decay algebraically with distance as ˜r-a . Mapping the problem onto two-dimensional Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a nontrivial fixed point which is stable for 0.995
Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model
Deng Dongling; Gu Shijian; Chen Jingling
2010-02-15
Recently Seevinck and Uffink argued that genuine multipartite entanglement (GME) had not been established in the experiments designed to confirm GME. In this paper, we use the Bell-type inequalities introduced by Seevinck and Svetlichny [M. Seevinck, G. Svetlichny, Phys. Rev. Lett. 89 (2002) 060401] to investigate the GME problem in the one-dimensional transverse-field Ising model. We show explicitly that the ground states of this model violate the inequality when the external transverse magnetic field is weak, which indicate that the ground states in this model with weak magnetic field are fully entangled. Since this model can be simulated with nuclear magnetic resonance, our results provide a fresh approach to experimental test of GME.
Liu, Y; Dilger, J P
1993-01-01
The Ising model of statistical physics provides a framework for studying systems of protomers in which nearest neighbors interact with each other. In this article, the Ising model is applied to the study of cooperative phenomena between ligand-gated ion channels. Expressions for the mean open channel probability, rho o, and the variance, sigma 2, are derived from the grand partition function. In the one-dimensional Ising model, interactions between neighboring open channels give rise to a sigmoidal rho o versus concentration curve and a nonquadratic relationship between sigma 2 and rho o. Positive cooperativity increases the slope at the midpoint of the rho o versus concentration curve, shifts the apparent binding affinity to lower concentrations, and increases the variance for a given rho o. Negative cooperativity has the opposite effects. Strong negative cooperativity results in a bimodal sigma 2 versus rho o curve. The slope of the rho o versus concentration curve increases linearly with the number of binding sites on a protomer, but the sigma 2 versus rho o relationship is independent of the number of ligand binding sites. Thus, the sigma 2 versus rho o curve provides unambiguous information about channel interactions. In the two-dimensional Ising model, rho o and sigma 2 are calculated numerically from a series expansion of the grand partition function appropriate for weak interactions. Virtually all of the features exhibited by the one-dimensional model are qualitatively present in the two-dimensional model. These models are also applicable to voltage-gated ion channels. PMID:7679298
Rényi entropy of a line in two-dimensional Ising models
NASA Astrophysics Data System (ADS)
Stéphan, J.-M.; Misguich, G.; Pasquier, V.
2010-09-01
We consider the two-dimensional Ising model on an infinitely long cylinder and study the probabilities pi to observe a given spin configuration i along a circular section of the cylinder. These probabilities also occur as eigenvalues of reduced density matrices in some Rokhsar-Kivelson wave functions. We analyze the subleading constant to the Rényi entropy Rn=1/(1-n)ln(∑ipin) and discuss its scaling properties at the critical point. Studying three different microscopic realizations, we provide numerical evidence that it is universal and behaves in a steplike fashion as a function of n with a discontinuity at the Shannon point n=1 . As a consequence, a field theoretical argument based on the replica trick would fail to give the correct value at this point. We nevertheless compute it numerically with high precision. Two other values of the Rényi parameter are of special interest: n=1/2 and n=∞ are related in a simple way to the Affleck-Ludwig boundary entropies associated to free and fixed boundary conditions, respectively.
Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models.
Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; Macrì, Tommaso; Lahaye, Thierry; Browaeys, Antoine
2016-06-30
Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism. PMID:27281203
Johnson, Jason K; Chertkov, Michael; Netrapalli, Praneeth
2010-11-12
Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus our attention on the class of planar Ising models, for which inference is tractable using techniques of statistical physics [Kac and Ward; Kasteleyn]. Based on these techniques and recent methods for planarity testing and planar embedding [Chrobak and Payne], we propose a simple greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. We present the results of numerical experiments evaluating the performance of our algorithm.
NASA Astrophysics Data System (ADS)
Liu, Cheng-cheng; Shi, Jia-dong; Ding, Zhi-yong; Ye, Liu
2016-08-01
In this paper, the effect of external magnet field g on the relationship among the quantum discord, Bell non-locality and quantum phase transition by employing quantum renormalization-group (QRG) method in the one-dimensional transverse Ising model is investigated. In our model, external magnet field g can influence the phase diagrams. The results have shown that both the two quantum correlation measures can develop two saturated values, which are associated with two distinct phases: long-ranged ordered Ising phase and the paramagnetic phase with the number of QRG iterations increasing. Additionally, quantum non-locality always existent in the long-ranged ordered Ising phase no matter whatever the value of g is and what times QRG steps are carried out and we conclude that the quantum non-locality always exists not only suitable for the two sites of block, but for nearest-neighbor blocks in the long-ranged ordered Ising phase. However, the block-block correlation in the paramagnetic phase is not strong enough to violate the Bell-CHSH inequality as the size of system becomes large. Furthermore, when the system violates the CHSH inequality, i.e., satisfies quantum non-locality, it needs to be entangled. On the other way, if the system obeys the CHSH inequality, it may be entangled or not. To gain further insight, the non-analytic and scaling behavior of QD and Bell non-locality have also been analyzed in detail and this phenomenon indicates that the behavior of the correlation can perfectly help one to observe the quantum critical properties of the model.
NASA Astrophysics Data System (ADS)
Park, Sung-Been; Cha, Min-Chul
2015-11-01
We investigate the finite-size scaling properties of the quantum phase transition in the one-dimensional quantum Ising model with periodic boundary conditions by representing the ground state in matrix product state forms. The infinite time-evolving block decimation technique is used to optimize the states. A trace over a product of the matrices multiplied as many times as the number of sites yields the finite-size effects. For sufficiently large Schmidt ranks, the finite-size scaling behavior determines the critical point and the critical exponents whose values are consistent with the analytical results.
Topological Characterization of Extended Quantum Ising Models
NASA Astrophysics Data System (ADS)
Zhang, G.; Song, Z.
2015-10-01
We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic X Y model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the X Y model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.
Topological Characterization of Extended Quantum Ising Models.
Zhang, G; Song, Z
2015-10-23
We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram. PMID:26551140
Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model
Morales, Irving O.; Landa, Emmanuel; Angeles, Carlos Calderon; Toledo, Juan C.; Rivera, Ana Leonor; Temis, Joel Mendoza; Frank, Alejandro
2015-01-01
Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point. PMID:26103513
Studies of hysteresis in two-dimensional kinetic Ising model using the FORC technique
NASA Astrophysics Data System (ADS)
Robb, Daniel; Novotny, Mark; Rikvold, Per Arne
2004-03-01
We describe the FORC (first order reversal curve) technique [1] for hysteresis, first developed as an experimental method to better characterize magnetic materials, and present FORC distributions for simulations of a square-lattice kinetic Ising model. To understand the simulation results, we apply a theory of magnetization reversal for the multidroplet (MD) regime [2] for homogeneous nucleation and growth, also called the Kolmogorov-Johnson-Mehl-Avrami regime. The FORC `partial hysteresis' loops exhibit different properties than those of systems with strong disorder [1]. We compare the simulation and the theory for several lattice sizes, frequencies of the external field, and temperatures. [1] C.R. Pike, A.P. Roberts, and K.L. Verosub, J. Appl. Phys. 85, 6660 (1999). [2] S.W. Sides, P.A. Rikvold, and M.A. Novotny, Phys. Rev. E 59, 2710 (1999).
Two-dimensional Ising transition through a technique from two-state opinion-dynamics models
NASA Astrophysics Data System (ADS)
Galam, Serge; Martins, André C. R.
2015-01-01
The Ising ferromagnetic model on a square lattice is revisited using the Galam unifying frame (GUF), set to investigate two-state opinion-dynamics models. When combined with Metropolis dynamics, an unexpected intermediate "dis/order" regime is found with the coexistence of two attractors associated, respectively, to an ordered and a disordered phases. The basin of attraction of initial conditions for the disordered phase attractor starts from zero size at a first critical temperature Tc 1 to embody the total landscape of initial conditions at a second critical temperature Tc 2, with Tc 1≈1.59 and Tc 2≈2.11 in J /kB units. It appears that Tc 2 is close to the Onsager result Tc≈2.27 . The transition, which is first-order-like, exhibits a vertical jump to the disorder phase at Tc 2, reminiscent of the rather abrupt vanishing of the corresponding Onsager second-order transition. However, using Glauber dynamics combined with GUF does not yield the intermediate phase and instead the expected classical mean-field transition is recovered at Tc≈3.09 . Accordingly, although the "dis/order" regime produced by the GUF-Metropolis combination is not physical, it is an intriguing result to be understood. In particular the fact that Glauber and Metropolis dynamics yield so different results using GUF needs an explanation. The possibility of extending GUF to larger clusters is discussed.
Monte Carlo investigation of critical dynamics in the three-dimensional Ising model
NASA Astrophysics Data System (ADS)
Wansleben, S.; Landau, D. P.
1991-03-01
We report the results of a Monte Carlo investigation of the (equilibrium) time-displaced correlation functions for the magnetization and energy of a simple cubic Ising model as a function of time, temperature, and lattice size. The simulations were carried out on a CDC CYBER 205 supercomputer employing a high-speed, vectorized multispin coding program and using a total of 5×1012 Monte Carlo spin-flip trials. We used L×L×L lattices with periodic boundary conditions and L as large as 96. The short-time and long-time behaviors of the correlation functions are analyzed by fits to a sum of exponential decays, and the critical exponent z for the largest relaxation time is extracted using a finite-size-scaling analysis. Our estimate z=2.04+/-0.03 resolves an intriguing contradiction in the literature; it satisfies the theoretical lower bound and is in agreement with the prediction obtained by ɛ expansion. We also consider various small systematic errors that typically occur in the analysis of relaxation functions and show how they can lead to spurious results if sufficient care is not exercised.
Two-dimensional Ising transition through a technique from two-state opinion-dynamics models.
Galam, Serge; Martins, André C R
2015-01-01
The Ising ferromagnetic model on a square lattice is revisited using the Galam unifying frame (GUF), set to investigate two-state opinion-dynamics models. When combined with Metropolis dynamics, an unexpected intermediate "dis/order" regime is found with the coexistence of two attractors associated, respectively, to an ordered and a disordered phases. The basin of attraction of initial conditions for the disordered phase attractor starts from zero size at a first critical temperature T(c1) to embody the total landscape of initial conditions at a second critical temperature T(c2), with T(c1)≈1.59 and T(c2)≈2.11 in J/k(B) units. It appears that T(c2) is close to the Onsager result T(c)≈2.27. The transition, which is first-order-like, exhibits a vertical jump to the disorder phase at T(c2), reminiscent of the rather abrupt vanishing of the corresponding Onsager second-order transition. However, using Glauber dynamics combined with GUF does not yield the intermediate phase and instead the expected classical mean-field transition is recovered at T(c)≈3.09. Accordingly, although the "dis/order" regime produced by the GUF-Metropolis combination is not physical, it is an intriguing result to be understood. In particular the fact that Glauber and Metropolis dynamics yield so different results using GUF needs an explanation. The possibility of extending GUF to larger clusters is discussed. PMID:25679571
NASA Astrophysics Data System (ADS)
Kizilirmak, Ganimet Mülazımoğlu
2015-12-01
The four-dimensional Ising model is simulated on the Creutz cellular automaton (CCA) near the infinite-lattice critical temperature for the lattice with the linear dimension 4 ⩽ L ⩽ 22. The temperature dependence of Binder parameter ( g L) are analyzed for the lattice with the linear dimension 4 ⩽ L ⩽ 22. In this study conducted highly detailed, two different types of behavior were determined as a result of varying linear lattice dimension. The infinite lattice critical temperatures are obtained to be T c = 6.6845 ± 0.0005 in interval 4 ⩽ L ⩽ 12 and T c = 6.6807 ± 0.0024 in interval 14 ⩽ L ⩽ 22. The finite and infinite lattice critical exponents for the order parameter, the magnetic susceptibility and the specific heat are computed from the results of simulations by using finite-size scaling relations. Critical linear lattice size have been identified as L = 14.
Ising and dimer models in two and three dimensions
NASA Astrophysics Data System (ADS)
Moessner, R.; Sondhi, S. L.
2003-08-01
Motivated by recent interest in 2+1 dimensional quantum dimer models, we revisit Fisher’s mapping of two-dimensional Ising models to hardcore dimer models. First, we note that the symmetry breaking transition of the ferromagnetic Ising model maps onto a non-symmetry breaking transition in dimer language—instead it becomes a deconfinement transition for test monomers. Next, we introduce a modification of Fisher’s mapping in which a second dimer model, also equivalent to the Ising model, is defined on a generically different lattice derived from the dual. In contrast to Fisher’s original mapping, this enables us to reformulate frustrated Ising models as dimer models with positive weights and we illustrate this by providing a new solution of the fully frustrated Ising model on the square lattice. Finally, by means of the modified mapping we show that a large class of three-dimensional Ising models are precisely equivalent, in the time continuum limit, to particular quantum dimer models. As Ising models in three dimensions are dual to Ising gauge theories, this further yields an exact map between the latter and the quantum dimer models. The paramagnetic phase in Ising language maps onto a deconfined, topologically ordered phase in the dimer models. Using this set of ideas, we also construct an exactly soluble quantum eight vertex model.
Montakhab, Afshin; Asadian, Ali
2010-12-15
In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two, and three dimensions from a multipartite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric Greenberger-Horne-Zeilinger-like state to a paramagnetic product state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one- and two-dimensional models. Our results indicate that such multipartite measure of global entanglement shows universal features regardless of dimension d. Our results also provide evidence that multipartite entanglement is better suited for the study of quantum phase transitions than the much-studied bipartite measures.
Navas-Portella, Víctor; Vives, Eduard
2016-02-01
This work studies universal finite size scaling functions for the number of one-dimensional spanning avalanches in a two-dimensional (2D) disordered system with boundary conditions of different nature and different aspect ratios. To this end, we will consider the 2D random field Ising model at T=0 driven by the external field H with athermal dynamics implemented with periodic and forced boundary conditions. We have chosen a convenient scaling variable z that accounts for the deformation of the distance to the critical point caused by the aspect ratio. In addition, assuming that the dependence of the finite size scaling functions on the aspect ratio can be accounted for by an additional multiplicative factor, we have been able to collapse data for different system sizes, different aspect ratios, and different types of the boundary conditions into a single scaling function Q̂. PMID:26986310
On the dynamics of the Ising model of cooperative phenomena.
Montroll, E W
1981-01-01
A two-dimensional (and to some degree three-dimensional) version of Glauber's one-dimensional spin relaxation model is described. The model is constructed to yield the Ising model of cooperative phenomena at equilibrium. A complete hierarchy of differential equations for multispin correlation functions is constructed. Some remarks are made concerning the solution of them for the initial value problem of determining the relaxation of an initial set of spin distributions. PMID:16592955
On the Dynamics of the Ising Model of Cooperative Phenomena
NASA Astrophysics Data System (ADS)
Montroll, Elliott W.
1981-01-01
A two-dimensional (and to some degree three-dimensional) version of Glauber's one-dimensional spin relaxation model is described. The model is constructed to yield the Ising model of cooperative phenomena at equilibrium. A complete hierarchy of differential equations for multispin correlation functions is constructed. Some remarks are made concerning the solution of them for the initial value problem of determining the relaxation of an initial set of spin distributions.
On the dynamics of the Ising model of cooperative phenomena
Montroll, Elliott W.
1981-01-01
A two-dimensional (and to some degree three-dimensional) version of Glauber's one-dimensional spin relaxation model is described. The model is constructed to yield the Ising model of cooperative phenomena at equilibrium. A complete hierarchy of differential equations for multispin correlation functions is constructed. Some remarks are made concerning the solution of them for the initial value problem of determining the relaxation of an initial set of spin distributions. PMID:16592955
Sheared Ising models in three dimensions
NASA Astrophysics Data System (ADS)
Hucht, Alfred; Angst, Sebastian
2013-03-01
The nonequilibrium phase transition in sheared three-dimensional Ising models is investigated using Monte Carlo simulations in two different geometries corresponding to different shear normals [A. Hucht and S. Angst, EPL 100, 20003 (2012)]. We demonstrate that in the high shear limit both systems undergo a strongly anisotropic phase transition at exactly known critical temperatures Tc which depend on the direction of the shear normal. Using dimensional analysis, we determine the anisotropy exponent θ = 2 as well as the correlation length exponents ν∥ = 1 and ν⊥ = 1 / 2 . These results are verified by simulations, though considerable corrections to scaling are found. The correlation functions perpendicular to the shear direction can be calculated exactly and show Ornstein-Zernike behavior. Supported by CAPES-DAAD through PROBRAL as well as by the German Research Society (DFG) through SFB 616 ``Energy Dissipation at Surfaces.''
Ising model for distribution networks
NASA Astrophysics Data System (ADS)
Hooyberghs, H.; Van Lombeek, S.; Giuraniuc, C.; Van Schaeybroeck, B.; Indekeu, J. O.
2012-01-01
An elementary Ising spin model is proposed for demonstrating cascading failures (breakdowns, blackouts, collapses, avalanches, etc.) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidarity environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters.
Some Fruits of Genius: Lars Onsager and the Ising Model
NASA Astrophysics Data System (ADS)
Fisher, Michael E.
2006-03-01
The story of the exact solution of the two-dimensional Ising model by Lars Onsager in the 1940's will be sketched and some of the striking developments following from it, especially for the behavior of fluctuating interfaces, will be recounted.
Ising Model Reprogramming of a Repeat Protein's Equilibrium Unfolding Pathway.
Millership, C; Phillips, J J; Main, E R G
2016-05-01
Repeat proteins are formed from units of 20-40 aa that stack together into quasi one-dimensional non-globular structures. This modular repetitive construction means that, unlike globular proteins, a repeat protein's equilibrium folding and thus thermodynamic stability can be analysed using linear Ising models. Typically, homozipper Ising models have been used. These treat the repeat protein as a series of identical interacting subunits (the repeated motifs) that couple together to form the folded protein. However, they cannot describe subunits of differing stabilities. Here we show that a more sophisticated heteropolymer Ising model can be constructed and fitted to two new helix deletion series of consensus tetratricopeptide repeat proteins (CTPRs). This analysis, showing an asymmetric spread of stability between helices within CTPR ensembles, coupled with the Ising model's predictive qualities was then used to guide reprogramming of the unfolding pathway of a variant CTPR protein. The designed behaviour was engineered by introducing destabilising mutations that increased the thermodynamic asymmetry within a CTPR ensemble. The asymmetry caused the terminal α-helix to thermodynamically uncouple from the rest of the protein and preferentially unfold. This produced a specific, highly populated stable intermediate with a putative dimerisation interface. As such it is the first step in designing repeat proteins with function regulated by a conformational switch. PMID:26947150
Numerical tests of nucleation theories for the Ising models
NASA Astrophysics Data System (ADS)
Ryu, Seunghwa; Cai, Wei
2010-07-01
The classical nucleation theory (CNT) is tested systematically by computer simulations of the two-dimensional (2D) and three-dimensional (3D) Ising models with a Glauber-type spin flip dynamics. While previous studies suggested potential problems with CNT, our numerical results show that the fundamental assumption of CNT is correct. In particular, the Becker-Döring theory accurately predicts the nucleation rate if the correct droplet free energy function is provided as input. This validates the coarse graining of the system into a one dimensional Markov chain with the largest droplet size as the reaction coordinate. Furthermore, in the 2D Ising model, the droplet free energy predicted by CNT matches numerical results very well, after a logarithmic correction term from Langer’s field theory and a constant correction term are added. But significant discrepancies are found between the numerical results and existing theories on the magnitude of the logarithmic correction term in the 3D Ising model. Our analysis underscores the importance of correctly accounting for the temperature dependence of surface energy when comparing numerical results and nucleation theories.
Antiferromagnetic Ising Model in Hierarchical Networks
NASA Astrophysics Data System (ADS)
Cheng, Xiang; Boettcher, Stefan
2015-03-01
The Ising antiferromagnet is a convenient model of glassy dynamics. It can introduce geometric frustrations and may give rise to a spin glass phase and glassy relaxation at low temperatures [ 1 ] . We apply the antiferromagnetic Ising model to 3 hierarchical networks which share features of both small world networks and regular lattices. Their recursive and fixed structures make them suitable for exact renormalization group analysis as well as numerical simulations. We first explore the dynamical behaviors using simulated annealing and discover an extremely slow relaxation at low temperatures. Then we employ the Wang-Landau algorithm to investigate the energy landscape and the corresponding equilibrium behaviors for different system sizes. Besides the Monte Carlo methods, renormalization group [ 2 ] is used to study the equilibrium properties in the thermodynamic limit and to compare with the results from simulated annealing and Wang-Landau sampling. Supported through NSF Grant DMR-1207431.
Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
NASA Astrophysics Data System (ADS)
Hesselmann, S.; Wessel, S.
2016-04-01
The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the underlying quantum critical point. Here, we employ quantum Monte Carlo simulations to examine these relations in detail for two-dimensional quantum systems that exhibit a finite-temperature Ising-transition line in the vicinity of a quantum critical point that belongs to the universality class of either (i) the three-dimensional Ising model for the case of the quantum Ising model in a transverse magnetic field on the square lattice or (ii) the chiral Ising transition for the case of a half-filled system of spinless fermions on the honeycomb lattice with nearest-neighbor repulsion. While the first case allows large-scale simulations to assess the scaling predictions to a high precision in terms of the known values for the critical exponents at the quantum critical point, for the later case, we extract values of the critical exponents ν and η , related to the order parameter fluctuations, which we discuss in relation to other recent estimates from ground-state quantum Monte Carlo calculations as well as analytical approaches.
The Ising Model in Physics and Statistical Genetics
Majewski, Jacek; Li, Hao; Ott, Jurg
2001-01-01
Interdisciplinary communication is becoming a crucial component of the present scientific environment. Theoretical models developed in diverse disciplines often may be successfully employed in solving seemingly unrelated problems that can be reduced to similar mathematical formulation. The Ising model has been proposed in statistical physics as a simplified model for analysis of magnetic interactions and structures of ferromagnetic substances. Here, we present an application of the one-dimensional, linear Ising model to affected-sib-pair (ASP) analysis in genetics. By analyzing simulated genetics data, we show that the simplified Ising model with only nearest-neighbor interactions between genetic markers has statistical properties comparable to much more complex algorithms from genetics analysis, such as those implemented in the Allegro and Mapmaker-Sibs programs. We also adapt the model to include epistatic interactions and to demonstrate its usefulness in detecting modifier loci with weak individual genetic contributions. A reanalysis of data on type 1 diabetes detects several susceptibility loci not previously found by other methods of analysis. PMID:11517425
Information geometry of the ising model on planar random graphs.
Janke, W; Johnston, D A; Malmini, Ranasinghe P K C
2002-11-01
It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterization of the phase structure, particularly in the case where there are two such parameters, such as the Ising model with inverse temperature beta and external field h. In various two-parameter calculable models, the scalar curvature R of the information metric has been found to diverge at the phase transition point beta(c) and a plausible scaling relation postulated: R approximately |beta-beta(c)|(alpha-2). For spin models the necessity of calculating in nonzero field has limited analytic consideration to one-dimensional, mean-field and Bethe lattice Ising models. In this paper we use the solution in field of the Ising model on an ensemble of planar random graphs (where alpha=-1, beta=1/2, gamma=2) to evaluate the scaling behavior of the scalar curvature, and find R approximately |beta-beta(c)|(-2). The apparent discrepancy is traced back to the effect of a negative alpha. PMID:12513568
NASA Astrophysics Data System (ADS)
Douthett, Elwood (Jack) Moser, Jr.
1999-10-01
Cyclic configurations of white and black sites, together with convex (concave) functions used to weight path length, are investigated. The weights of the white set and black set are the sums of the weights of the paths connecting the white sites and black sites, respectively, and the weight between sets is the sum of the weights of the paths that connect sites opposite in color. It is shown that when the weights of all configurations of a fixed number of white and a fixed number of black sites are compared, minimum (maximum) weight of a white set, minimum (maximum) weight of the a black set, and maximum (minimum) weight between sets occur simultaneously. Such configurations are called maximally even configurations. Similarly, the configurations whose weights are the opposite extremes occur simultaneously and are called minimally even configurations. Algorithms that generate these configurations are constructed and applied to the one- dimensional antiferromagnetic spin-1/2 Ising model. Next the goodness of continued fractions as applied to musical intervals (frequency ratios and their base 2 logarithms) is explored. It is shown that, for the intermediate convergents between two consecutive principal convergents of an irrational number, the first half of the intermediate convergents are poorer approximations than the preceding principal convergent while the second half are better approximations; the goodness of a middle intermediate convergent can only be determined by calculation. These convergents are used to determine what equal-tempered systems have intervals that most closely approximate the musical fifth (pn/ qn = log2(3/2)). The goodness of exponentiated convergents ( 2pn/qn~3/2 ) is also investigated. It is shown that, with the exception of a middle convergent, the goodness of the exponential form agrees with that of its logarithmic Counterpart As in the case of the logarithmic form, the goodness of a middle intermediate convergent in the exponential form can
Some results on hyperscaling in the 3D Ising model
Baker, G.A. Jr.; Kawashima, Naoki
1995-09-01
The authors review exact studies on finite-sized 2 dimensional Ising models and show that the point for an infinite-sized model at the critical temperature is a point of nonuniform approach in the temperature-size plane. They also illuminate some strong effects of finite-size on quantities which do not diverge at the critical point. They then review Monte Carlo studies for 3 dimensional Ising models of various sizes (L = 2--100) at various temperatures. From these results they find that the data for the renormalized coupling constant collapses nicely when plotted against the correlation length, determined in a system of edge length L, divided by L. They also find that {zeta}{sub L}/L {ge} 0.26 is definitely too large for reliable studies of the critical value, g*, of the renormalized coupling constant. They have reasonable evidence that {zeta}{sub L}/L {approx} 0.1 is adequate for results that are within one percent of those for the infinite system size. On this basis, they have conducted a series of Monte Carlo calculations with this condition imposed. These calculations were made practical by the development of improved estimators for use in the Swendsen-Wang cluster method. The authors found from these results, coupled with a reversed limit computation (size increases with the temperature fixed at the critical temperature), that g* > 0, although there may well be a sharp downward drop in g as the critical temperature is approached in accord with the predictions of series analysis. The results support the validity of hyperscaling in the 3 dimensional Ising model.
Networked Ising-Sznajd AR-β Model
NASA Astrophysics Data System (ADS)
Nagao, Tomonori; Ohmiya, Mayumi
2009-09-01
The modified Ising-Sznajd model is studied to clarify the machanism of price formation in the stock market. The conventional Ising-Sznajd model is improved as a small world network with the rewireing probability β(t) which depends on the time. Numerical experiments show that phase transition, regarded as a economical crisis, is inevitable in this model.
Exact ground states of large two-dimensional planar Ising spin glasses
NASA Astrophysics Data System (ADS)
Pardella, G.; Liers, F.
2008-11-01
Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 30002 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the L. Bieche approach.
Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt
2014-08-01
We present a study of the critical behavior of the Blume-Capel model with three spin states (S=±1,0) confined between parallel walls separated by a distance L where competitive surface magnetic fields act. By properly choosing the crystal field (D), which regulates the density of nonmagnetic species (S=0), such that those impurities are excluded from the bulk (where D=-∞) except in the middle of the sample [where D(M)(L/2)≠-∞], we are able to control the presence of a defect line in the middle of the sample and study its influence on the interface between domains of different spin orientations. So essentially we study an Ising model with a defect line but, unlike previous work where defect lines in Ising models were defined via weakened bonds, in the present case the defect line is due to mobile vacancies and hence involves additional entropy. In this way, by drawing phase diagrams, i.e., plots of the wetting critical temperature (T(w)) versus the magnitude of the crystal field at the middle of the sample (D(M)), we observe curves of (first-) second-order wetting transitions for (small) high values of D(M). Theses lines meet in tricritical wetting points, i.e., (T(w)(tc),D(M)(tc)), which also depend on the magnitude of the surface magnetic fields. It is found that second-order wetting transitions satisfy the scaling theory for short-range interactions, while first-order ones do not exhibit hysteresis, provided that small samples are used, since fluctuations wash out hysteretic effects. Since hysteresis is observed in large samples, we performed extensive thermodynamic integrations in order to accurately locate the first-order transition points, and a rather good agreement is found by comparing such results with those obtained just by observing the jump of the order parameter in small samples. PMID:25215741
Applying Tabu Search to the Two-Dimensional Ising Spin Glass
NASA Astrophysics Data System (ADS)
Laguna, Manuel; Laguna, Pablo
A variety of problems in statistical physics, such as Ising-like systems, can be modeled as integer programs. Physicists have relied mostly on Monte Carlo methods to find approximate solutions to these computationally difficult problems. In some cases, optimal solutions to relatively small problems have been found using standard optimization techniques, e.g., cutting plane and branch-and-bound algorithms. Motivated by the success of tabu search (TS) in finding optimal or near-optimal solutions to combinatorial optimization problems in a number of different settings, we study the application of this methodology to Ising-like systems. Particularly, we develop a TS method to find ground states of two-dimensional spin glasses. Our method performs a search at different levels of resolution in the spin lattice, and it is designed to obtain optimal or near-optimal solutions to problem instances with several different characteristics. Results are reported for computational experiments with up to 64×64 lattices.
The Worm Process for the Ising Model is Rapidly Mixing
NASA Astrophysics Data System (ADS)
Collevecchio, Andrea; Garoni, Timothy M.; Hyndman, Timothy; Tokarev, Daniel
2016-07-01
We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.
The Worm Process for the Ising Model is Rapidly Mixing
NASA Astrophysics Data System (ADS)
Collevecchio, Andrea; Garoni, Timothy M.; Hyndman, Timothy; Tokarev, Daniel
2016-09-01
We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.
Ising tricriticality in the extended Hubbard model with bond dimerization
NASA Astrophysics Data System (ADS)
Ejima, Satoshi; Essler, Fabian H. L.; Lange, Florian; Fehske, Holger
2016-06-01
We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c =7 /10 . Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results.
NASA Astrophysics Data System (ADS)
Miwa, Tetsuji
2013-03-01
Studies on integrable models in statistical mechanics and quantum field theory originated in the works of Bethe on the one-dimensional quantum spin chain and the work of Onsager on the two-dimensional Ising model. I will talk on the discovery in 1977 of the link between quantum field theory in the scaling limit of the two-dimensional Ising model and the theory of monodromy preserving linear ordinary differential equations. This work was the staring point of our journey with Michio Jimbo in integrable models, the journey which finally led us to the exact results on the correlation functions of quantum spin chains in 1992.
NASA Astrophysics Data System (ADS)
Horowitz, C. M.; Bab, M. A.; Mazzini, M.; Puzzo, M. L. Rubio; Saracco, G. P.
2015-10-01
The ferromagnetic Ising model with antiferromagnetic dipole interactions is investigated by means of Monte Carlo simulations, focusing on the characterization of the phase transitions between the tetragonal liquid and stripe of width h phases. The dynamic evolution of the physical observables is analyzed within the short-time regime for 0.5 ≤δ ≤1.3 , where δ is the ratio between the short-range exchange and the long-range dipole interaction constants. The obtained results for the interval 0.5 ≤δ ≤1.2 indicate that the phase transition line between the h =1 stripe and tetragonal liquid phases is continuous. This finding contributes to clarifying the controversy about the order of this transition. This controversy arises from the difficulties introduced in the simulations due to the presence of long-range dipole interactions, such as an important increase in the simulation times that limits the system size used, strong finite size effects, as well as to the existence of multiple metastable states at low temperatures. The study of the short-time dynamics of the model allows us to avoid these hindrances. Moreover, due to the fact that the finite-size effects do not significantly affect the power-law behavior exhibited in the observables within the short-time regime, the results could be attributed to those corresponding to the thermodynamic limit. As a consequence of this, a careful characterization of the critical behavior for the whole transition line is performed by giving the complete set of critical exponents.
Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices
NASA Astrophysics Data System (ADS)
Ananikian, N. S.; Ananikyan, L. N.; Chakhmakhchyan, L. A.
2011-09-01
The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by the recurrence relation method in the antiferromagnetic Q-state Potts model on the Bethe lattice (at Q < 2) and in the antiferromagnetic Ising model with three-site interaction on the Husimi cactus. The Lyapunov exponents have been calculated, modulated phases and a chaotic regime in the cyclic period-3 window have been found for one-dimensional rational mappings determined the properties of these systems.
Scaling functions in the square Ising model
NASA Astrophysics Data System (ADS)
Hassani, S.; Maillard, J.-M.
2015-03-01
We show and give the linear differential operators Lqscal of order q={{n}2}/4+n+7/8+{{(-1)}n}/8, for the integrals {{I}n}(r) which appear in the two-point correlation scaling function of Ising model \\{{F}+/- }(r)={{lim }scaling}M+/- -2 \\lt {{σ }0,0} {{σ }M,N}\\gt ={{\\sum }n}{{I}n}(r). The integrals {{I}n}(r) are given in expansion around r=0 in the basis of the formal solutions of Lqscal with transcendental combination coefficients. We find that the expression {{r}1/4}exp ({{r}2}/8) is a solution of the Painlevé VI equation in the scaling limit. Combinations of the (analytic at r=0) solutions of Lqscal sum to exp ({{r}2}/8). We show that the expression {{r}1/4}exp ({{r}2}/8) is the scaling limit of the correlation function C(N,N) and C(N,N+1). The differential Galois groups of the factors occurring in the operators Lqscal are given.
Toward an Ising Model of Cancer and Beyond
Torquato, Salvatore
2011-01-01
The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an “Ising model” of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell
Toward an Ising model of cancer and beyond
NASA Astrophysics Data System (ADS)
Torquato, Salvatore
2011-02-01
The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review the research work that we have done toward the development of an 'Ising model' of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which cells transition between states (proliferative, hypoxic and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to study the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility
Toward an Ising model of cancer and beyond.
Torquato, Salvatore
2011-02-01
The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review the research work that we have done toward the development of an 'Ising model' of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which cells transition between states (proliferative, hypoxic and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to study the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility
Ising-model description of long-range correlations in DNA sequences
NASA Astrophysics Data System (ADS)
Colliva, A.; Pellegrini, R.; Testori, A.; Caselle, M.
2015-05-01
We model long-range correlations of nucleotides in the human DNA sequence using the long-range one-dimensional (1D) Ising model. We show that, for distances between 103 and 106 bp, the correlations show a universal behavior and may be described by the non-mean-field limit of the long-range 1D Ising model. This allows us to make some testable hypothesis on the nature of the interaction between distant portions of the DNA chain which led to the DNA structure that we observe today in higher eukaryotes.
Droplet model for autocorrelation functions in an Ising ferromagnet
NASA Technical Reports Server (NTRS)
Tang, Chao; Nakanishi, Hiizu; Langer, J. S.
1989-01-01
The autocorrelation function of Ising spins in an ordered phase is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation which describes fluctuations in the radius of a single droplet is studied in detail. A general description of the transformation to a Fokker-Planck equations and the ways in which a spectral analysis of that equation can be used to compute the autocorrelation function is given. It is shown that the eigenvalues of the Fokker-Planck operator form (1) a continuous spectrum of relaxation rates starting from zero for d = 2, (2) a continuous spectrum with a finite gap for d = 3, and (3) a discrete spectrum for d greater than 4, where d is the spatial dimensionality. Detailed solutions for various cases are presented.
Long range Ising model for credit risk modeling
NASA Astrophysics Data System (ADS)
Molins, Jordi; Vives, Eduard
2005-07-01
Within the framework of maximum entropy principle we show that the finite-size long-range Ising model is the adequate model for the description of homogeneous credit portfolios and the computation of credit risk when default correlations between the borrowers are included. The exact analysis of the model suggest that when the correlation increases a first-order-like transition may occur inducing a sudden risk increase.
Complex zeros of the 2 d Ising model on dynamical random lattices
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
1998-04-01
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2 d quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two matrix model and by Monte Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional patterns in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of singularities near the critical point.
Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6
NASA Astrophysics Data System (ADS)
Robinson, Neil J.; Essler, Fabian H. L.; Cabrera, Ivelisse; Coldea, Radu
2014-11-01
We present experimental and theoretical evidence that an interesting quantum many-body effect—quasiparticle breakdown—occurs in the quasi-one-dimensional spin-1/2 Ising-like ferromagnet CoNb2O6 in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of CoNb2O6 and determine the exchange parameters of this model by fitting the calculated single-particle dispersion to the one observed experimentally in applied transverse magnetic fields [1]. We present high-resolution inelastic neutron scattering measurements of the single-particle dispersion which observe "anomalous broadening" effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for nonzero matrix elements for decay by breaking the Z2 spin inversion symmetry of the Hamiltonian.
Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions
NASA Astrophysics Data System (ADS)
Alves, G. A.; Vasconcelos, M. S.; Alves, T. F. A.
2016-04-01
We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter qEA, the magnetic susceptibility χ , and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β ,γ , and ν . In the low-temperature limit we obtained a spin-glass phase with critical temperature around Tc≈2.274 , and the critical exponents β ,γ , and ν , indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model.
Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions.
Alves, G A; Vasconcelos, M S; Alves, T F A
2016-04-01
We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter q_{EA}, the magnetic susceptibility χ, and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β,γ, and ν. In the low-temperature limit we obtained a spin-glass phase with critical temperature around T_{c}≈2.274, and the critical exponents β,γ, and ν, indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model. PMID:27176258
Two-dimensional frustrated Ising network as an eigenvalue problem
NASA Astrophysics Data System (ADS)
Blackman, J. A.
1982-11-01
The Pfaffian method is used to study the square frustrated Ising network. The formalism is adapted in order to develop a relation with the problem of excitations in random alloys. It is shown that the counterpart of frustrated plaquettes are local modes within a band gap. Properties of the local modes are examined, including questions of gauge invariance and duality. Numerical calculations are done to investigate the way in which the local modes broaden into an impurity band.
The Critical Z-Invariant Ising Model via Dimers: Locality Property
NASA Astrophysics Data System (ADS)
Boutillier, Cédric; de Tilière, Béatrice
2011-01-01
We study a large class of critical two-dimensional Ising models, namely critical Z-invariant Ising models. Fisher (J Math Phys 7:1776-1781, 1966) introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer model corresponding to the critical Z-invariant Ising model, consisting of explicit expressions which only depend on the local geometry of the underlying isoradial graph. Our main result is an explicit local formula for the inverse Kasteleyn matrix, in the spirit of Kenyon (Invent Math 150(2):409-439, 2002), as a contour integral of the discrete exponential function of Mercat (Discrete period matrices and related topics, 2002) and Kenyon (Invent Math 150(2):409-439, 2002) multiplied by a local function. Using results of Boutillier and de Tilière (Prob Theor Rel Fields 147(3-4):379-413, 2010) and techniques of de Tilière (Prob Th Rel Fields 137(3-4):487-518, 2007) and Kenyon (Invent Math 150(2):409-439, 2002), this yields an explicit local formula for a natural Gibbs measure, and a local formula for the free energy. As a corollary, we recover Baxter's formula for the free energy of the critical Z-invariant Ising model (Baxter, in Exactly solved models in statistical mechanics, Academic Press, London, 1982), and thus a new proof of it. The latter is equal, up to a constant, to the logarithm of the normalized determinant of the Laplacian obtained in Kenyon (Invent Math 150(2):409-439, 2002).
Interacting damage models mapped onto ising and percolation models
Toussaint, Renaud; Pride, Steven R.
2004-03-23
The authors introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasistatic fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, they obtain the probability distribution of each damage configuration at any level of the imposed external deformation. They demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, they show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. they also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, they also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model
Interacting damage models mapped onto Ising and percolation models.
Toussaint, Renaud; Pride, Steven R
2005-04-01
We introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasi-static fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, we obtain the probability distribution of each damage configuration at any level of the imposed external deformation. We demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, we show that damage models with global load sharing are isomorphic to standard percolation theory and that damage models with a local load sharing rule are isomorphic to the standard Ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. We also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, we also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model to standard
An Ising model of transcription polarity in bacterial chromosomes
NASA Astrophysics Data System (ADS)
Baran, Robert H.; Ko, Hanseok
2006-04-01
Bacterial genes form clusters of the same transcription polarity and typically exhibit a preference to be coded on the leading strand of replication. An Ising model is proposed to quantify these two phenomena by analogy to the behavior of magnetic dipoles (spins) in a one-dimensional lattice. Corresponding to magnetic forces that co-orient adjacent spins and align them with an externally applied field, we imagine pseudo-forces that influence transcription polarity. Bonds of uniform strength {1}/{2} J between adjacent sites will model the adhesive (or repulsive) interactions while a polarity entraining force of strength H has the direction of replication. Ten bacterial chromosomes are reduced to spin configurations from which the model parameters are estimated by the method of maximum likelihood under the assumption of thermal equilibrium, following the application of established methods to locate replication origins and termini. χ 2-tests show that the model fits the data well in about half the cases but cluster size exhibits excess variance in general. These findings lead to a speculative interpretation of the pseudo-forces as the net effects of numerous insertions and deletions that succeed or fail according to their impact on the motions of enzymatic complexes involved in replication and transcription.
The gonihedric paradigm extension of the Ising model
NASA Astrophysics Data System (ADS)
Savvidy, George
2015-11-01
In this paper we review a recently suggested generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the partition function are analyzed. The model can also be formulated as a spin system with identical partition functions. The spin system represents a generalization of the Ising model with ferromagnetic, antiferromagnetic and quartic interactions. Higher symmetry of the model allows to construct dual spin systems in three and four dimensions. In three dimensions the transfer matrix describes the propagation of closed loops and we found its exact spectrum. It is a unique exact solution of the three-dimensional statistical spin system. In three and four dimensions, the system exhibits the second-order phase transitions. The gonihedric spin systems have exponentially degenerated vacuum states separated by the potential barriers and can be used as a storage of binary information.
Phase transitions in Ising models on directed networks.
Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof
2015-11-01
We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme. PMID:26651748
Phase transitions in Ising models on directed networks
NASA Astrophysics Data System (ADS)
Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof
2015-11-01
We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.
Topological defects on the lattice: I. The Ising model
NASA Astrophysics Data System (ADS)
Aasen, David; Mong, Roger S. K.; Fendley, Paul
2016-09-01
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang–Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers–Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.
Duality Between Spin Networks and the 2D Ising Model
NASA Astrophysics Data System (ADS)
Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.
2016-06-01
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.
Analytical properties of the anisotropic cubic Ising model
Hansel, D.; Maillard, J.M.; Oitmaa, J.; Velgakis, M.J.
1987-07-01
The authors combine an exact functional relation, the inversion relation, with conventional high-temperature expansions to explore the analytic properties of the anisotropic Ising model on both the square and simple cubic lattice. In particular, they investigate the nature of the singularities that occur in partially resummed expansions of the partition function and of the susceptibility.
Constrained variational problem with applications to the Ising model
NASA Astrophysics Data System (ADS)
Schonmann, Roberto H.; Shlosman, Senya B.
1996-06-01
We continue our study of the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic field h, initiated in our earlier work. We strengthen further a result previously proven by Martirosyan at low enough temperature, which roughly states that for finite systems with (-)-boundary conditions under a positive external field, the boundary effect dominates in the system if the linear size of the system is of order B/h with B small enough, while if B is large enough, then the external field dominates in the system. In our earlier work this result was extended to every subcritical value of the temperature. Here for every subcritical value of the temperature we show the existence of a critical value B 0 (T) which separates the two regimes specified above. We also find the asymptotic shape of the region occupied by the (+)-phase in the second regime, which turns out to be a "squeezed Wulff shape". The main step in our study is the solution of the variational problem of finding the curve minimizing the Wulff functional, which curve is constrained to the unit square. Other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, extended to all temperatures below the critical one.
Periodic Striped Ground States in Ising Models with Competing Interactions
NASA Astrophysics Data System (ADS)
Giuliani, Alessandro; Seiringer, Robert
2016-06-01
We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J c (p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J c (p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.
Critical behavior of the Ising model on random fractals
NASA Astrophysics Data System (ADS)
Monceau, Pascal
2011-11-01
We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension df≃1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ɛ expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.
The Ising Model on a Quenched Ensemble of c=-5 Gravity Graphs
NASA Astrophysics Data System (ADS)
Anagnostopoulos, K. N.; Bialas, P.; Thorleifsson, G.
1999-02-01
We study with Monte Carlo methods an ensemble of c=-5 gravity graphs, generated by coupling a conformal field theory with central charge c=-5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent γ s and the intrinsic fractal dimension d H. We find γ s=-1.5(1) and d H=3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, with a total central charge of the matter sector c=-5.
NASA Astrophysics Data System (ADS)
Neto, Minos A.; de Sousa, J. Ricardo; Padilha, Igor T.; Rodriguez Salmon, Octavio D.; Roberto Viana, J.; Dinóla Neto, F.
2016-06-01
We study the three-dimensional antiferromagnetic Ising model in both uniform longitudinal (H) and transverse (Ω) magnetic fields by using the effective-field theory (EFT) with finite cluster N = 1 spin (EFT-1). We analyzed the behavior of the magnetic susceptibility to investigate the reentrant phenomena that we have seen in the same phase diagram previously obtained in other papers. Our results shows the presence of two divergences in the susceptibility that indicates the existence of a reentrant behavior.
Two Dimensional Ising Superconductivity in Gated MoS2
NASA Astrophysics Data System (ADS)
Yuan, Noah; Lu, Jianming; Law, Kam Tuen; Zheliuk, Oleksandr; Leermakers, Inge; Zeitler, Ulrich; Ye, Jianting
The Zeeman effect, which is usually considered to be detrimental to superconductivity, can surprisingly protect the superconducting states created by gating a layered transition metal dichalcogenide. This effective Zeeman field, which is originated from intrinsic spin orbit coupling induced by breaking in-plane inversion symmetry, can reach nearly a hundred Tesla in magnitude. It strongly pins the spin orientation of the electrons to the out-of-plane directions and protects the superconductivity from being destroyed by an in-plane external magnetic field. In magnetotransport experiments of ionic-gate MoS2 transistors, where gating prepares individual superconducting state with different carrier doping, we indeed observe a spin-protected superconductivity by measuring an in-plane critical field Bc 2 far beyond the Pauli paramagnetic limit. The gating-enhanced Bc 2 is more than an order of magnitude larger compared to the bulk superconducting phases where the effective Zeeman field is weakened by interlayer coupling. Our study gives the first experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.
NASA Astrophysics Data System (ADS)
Cabrera, Ivelisse; Thompson, Jordan; Coldea, Radu; Robinson, Neil; Essler, Fabian; Prabhakaran, Dharmalingam; Bewley, Robert; Guidi, Tatiana
2013-03-01
The Ising chain in a transverse magnetic field is one of the canonical examples of a quantum phase transition. We have recently realized this model experimentally in the quasi-one-dimensional (1D) Ising-like ferromagnet CoNb2O6. Here, we present single-crystal inelastic neutron scattering measurements of the magnetic dispersion relations in the full three-dimensional (3D) Brillouin zone for magnetic fields near the critical point and in the high field paramagnetic phase. We explore the gap dependence as a function of field and quantify the cross-over to 3D physics at the lowest energies due to the finite interchain couplings. We parametrize the dispersion relations in the high-field paramagnetic phase to a spin wave model to quantify the sub-leading terms in the spin Hamiltonian beyond the dominant 1D Ising exchange.
A MATLAB GUI to study Ising model phase transition
NASA Astrophysics Data System (ADS)
Thornton, Curtislee; Datta, Trinanjan
We have created a MATLAB based graphical user interface (GUI) that simulates the single spin flip Metropolis Monte Carlo algorithm. The GUI has the capability to study temperature and external magnetic field dependence of magnetization, susceptibility, and equilibration behavior of the nearest-neighbor square lattice Ising model. Since the Ising model is a canonical system to study phase transition, the GUI can be used both for teaching and research purposes. The presence of a Monte Carlo code in a GUI format allows easy visualization of the simulation in real time and provides an attractive way to teach the concept of thermal phase transition and critical phenomena. We will also discuss the GUI implementation to study phase transition in a classical spin ice model on the pyrochlore lattice.
Information cascade, Kirman's ant colony model, and kinetic Ising model
NASA Astrophysics Data System (ADS)
Hisakado, Masato; Mori, Shintaro
2015-01-01
In this paper, we discuss a voting model in which voters can obtain information from a finite number of previous voters. There exist three groups of voters: (i) digital herders and independent voters, (ii) analog herders and independent voters, and (iii) tanh-type herders. In our previous paper Hisakado and Mori (2011), we used the mean field approximation for case (i). In that study, if the reference number r is above three, phase transition occurs and the solution converges to one of the equilibria. However, the conclusion is different from mean field approximation. In this paper, we show that the solution oscillates between the two states. A good (bad) equilibrium is where a majority of r select the correct (wrong) candidate. In this paper, we show that there is no phase transition when r is finite. If the annealing schedule is adequately slow from finite r to infinite r, the voting rate converges only to the good equilibrium. In case (ii), the state of reference votes is equivalent to that of Kirman's ant colony model, and it follows beta binomial distribution. In case (iii), we show that the model is equivalent to the finite-size kinetic Ising model. If the voters are rational, a simple herding experiment of information cascade is conducted. Information cascade results from the quenching of the kinetic Ising model. As case (i) is the limit of case (iii) when tanh function becomes a step function, the phase transition can be observed in infinite size limit. We can confirm that there is no phase transition when the reference number r is finite.
Phase transition of the Ising model on a fractal lattice.
Genzor, Jozef; Gendiar, Andrej; Nishino, Tomotoshi
2016-01-01
The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry. PMID:26871057
Phase transition of the Ising model on a fractal lattice
NASA Astrophysics Data System (ADS)
Genzor, Jozef; Gendiar, Andrej; Nishino, Tomotoshi
2016-01-01
The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.
Precision islands in the Ising and O( N ) models
NASA Astrophysics Data System (ADS)
Kos, Filip; Poland, David; Simmons-Duffin, David; Vichi, Alessandro
2016-08-01
We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, (Δ σ , Δ ɛ , λ σσɛ , λ ɛɛɛ ) = (0 .5181489(10) , 1 .412625(10) , 1 .0518537(41) , 1 .532435(19) , give the most precise determinations of these quantities to date.
Magnetization of the Ising model on the generalized checkerboard lattice
NASA Astrophysics Data System (ADS)
Lin, K. Y.; Wu, F. Y.
1988-08-01
We consider the Ising model on the generalized checkerboard lattice. Using a recent result by Baxter and Choy, we derive exact expressions for the magnetization of nodal spins at two values of the magnetic field, H=0 and H=i1/2 πkT. Our results are given in terms of Boltzmann weights of a unit cell of the checkerboard lattice without specifying its cell structures.
Ising model observables and non-backtracking walks
Helmuth, Tyler
2014-08-15
This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph G and the set of non-backtracking walks on G. The techniques used also give formulas for spin-spin correlation functions in terms of non-backtracking walks. The main tools used are Viennot's theory of heaps of pieces and turning numbers on surfaces.
NASA Technical Reports Server (NTRS)
Fitzenreiter, R. J.; Scudder, J. D.
1981-01-01
A computer package which produces contour plots of the three dimensional electron distribution function measured by an electron spectrometer aboard ISEE-1 is described. Examples of the contour plots and an explanation of how to use the program, including the necessary computer code for running the program on the GSFC 360/91 computer is presented. The method by which the discrete measurements of the distribution function, given by points on the four dimensional surface are synthesized into a smooth surface in a three dimensional space which can be contoured is described. The velocity components are parallel and perpendicular to the magnetic field, respectively, in the proper frame of the electrons.
Rényi information flow in the Ising model with single-spin dynamics.
Deng, Zehui; Wu, Jinshan; Guo, Wenan
2014-12-01
The n-index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase. PMID:25615223
Rényi information flow in the Ising model with single-spin dynamics
NASA Astrophysics Data System (ADS)
Deng, Zehui; Wu, Jinshan; Guo, Wenan
2014-12-01
The n -index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase.
Singularities of the Partition Function for the Ising Model Coupled to 2D Quantum Gravity
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2D quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We compute the zeros by using the exact solution coming from a two-matrix model and by Monte-Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near the critical point. Despite the small size of the systems studied, we can obtain a reasonable estimate of the (known) critical exponents.
Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt
2016-05-01
As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b, where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature T_{w} of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T. Also, precursor effects to droplet formation as T approaches T_{w} from below are studied. In accord with theoretical predictions, for T>T_{w} the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b^{1/2}). So, the area of the droplet is proportional to b^{3/2}, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied. PMID:27300962
NASA Astrophysics Data System (ADS)
Trobo, Marta L.; Albano, Ezequiel V.; Binder, Kurt
2016-05-01
As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b , where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature Tw of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T . Also, precursor effects to droplet formation as T approaches Tw from below are studied. In accord with theoretical predictions, for T >Tw the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b1 /2). So, the area of the droplet is proportional to b3 /2, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied.
Lateral critical Casimir force in two-dimensional inhomogeneous Ising strip. Exact results.
Nowakowski, Piotr; Napiórkowski, Marek
2016-06-01
We consider two-dimensional Ising strip bounded by two planar, inhomogeneous walls. The inhomogeneity of each wall is modeled by a magnetic field acting on surface spins. It is equal to +h1 except for a group of N1 neighboring surface spins where it is equal to -h1. The inhomogeneities of the upper and lower wall are shifted with respect to each other by a lateral distance L. Using exact diagonalization of the transfer matrix, we study both the lateral and normal critical Casimir forces as well as magnetization profiles for different temperature regimes: below the wetting temperature, between the wetting and the critical temperature, and above the critical temperature. The lateral critical Casimir force acts in the direction opposite to the shift L, and the excess normal force is always attractive. Upon increasing the shift L we observe, depending on the temperature regime, three different scenarios of breaking of the capillary bridge of negative magnetization connecting the inhomogeneities of the walls across the strip. As long as there exists a capillary bridge in the system, the magnitude of the excess total critical Casimir force is almost constant, with its direction depending on L. By investigating the bridge morphologies we have found a relation between the point at which the bridge breaks and the inflection point of the force. We provide a simple argument that some of the properties reported here should also hold for different models of the strip with the same type of inhomogeneity. PMID:27276962
Self-overlap as a method of analysis in Ising models.
Ferrera, A; Luque, B; Lacasa, L; Valero, E
2007-06-01
The damage spreading (DS) method provided a useful tool to obtain analytical results of the thermodynamics and stability of the two-dimensional (2D) Ising model--amongst many others--but it suffered both from ambiguities in its results and from large computational costs. In this paper we propose an alternative method, the so-called self-overlap method, based on the study of correlation functions measured at subsequent time steps as the system evolves towards its equilibrium. Applying Markovian and mean-field approximations to a 2D Ising system we obtain both analytical and numerical results on the thermodynamics that agree with the expected behavior. We also provide some analytical results on the stability of the system. Since only a single replica of the system needs to be studied, this method would seem to be free from the ambiguities that afflicted the DS method. It also seems to be numerically more efficient and analytically simpler. PMID:17677216
Interface localization in the 2D Ising model with a driven line
NASA Astrophysics Data System (ADS)
Cohen, O.; Mukamel, D.
2016-04-01
We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional biased Kawasaki dynamics in the central ring. Based on the exact solution of the two-dimensional Ising model, we are able to compute the phase diagram of the driven model within a special limit of fast drive and slow spin flips in the central ring. The model is found to exhibit two phases where the interface is pinned to the central ring: one in which it fluctuates symmetrically around the central ring and another where it fluctuates asymmetrically. In addition, we find a phase where the interface is centered in the bulk of the system, either below or above the central ring of the cylinder. In the latter case, the symmetry breaking is ‘stronger’ than that found in equilibrium when considering a repulsive potential on the central ring. This equilibrium model is analyzed here by using a restricted solid-on-solid model.
The sign-factor of the 3D Ising model on dual BCC lattice
NASA Astrophysics Data System (ADS)
Khachatryan, Sh.; Sedrakyan, A.
2002-01-01
We modify the two-dimensional model for the sign-factor of the regular 3D Ising model (3DIM) presented by Kavalov and Sedrakyan (Phys. Lett. 173B (1986) 449 and Nucl. Phys. 285B (1987) 264) for the case of dual to body centered cubic (DBCC) three-dimensional lattice. The advantage of this lattice is in an absence of self-intersections of the two-dimensional surfaces embedded there. We investigate simpler case of the model with scalar fermions (instead of SU(2) needed for 3DIM) and have found it's spectrum, which appeared to be massless. We reformulate the model by use of R-matrix formalism and a new interesting structure appears in a necessity to introduce three-particle R(3)ijk-matrices. We formulate the integrability property of the model for more general case.
NASA Technical Reports Server (NTRS)
Zhuang, H. C.; Russell, C. T.; Smith, E. J.; Gosling, J. T.
1981-01-01
The reported investigation is concerned with the propagation of the interplanetary shock waves in the solar wind and their three-dimensional interaction with the bow shock and magnetosheath. Formulae are deduced to predict the new position and orientation of the bow shock front after the interaction. To test the understanding of the interplanetary portion of the shock propagation, the obtained results are compared with observations on August 18, 1978, when both ISEE 1 and ISEE 3 were in the solar wind. Two examples of an interplanetary shock wave penetrating into the magnetosphere on October 4, 1978, and August 27, 1978, are examined, taking into account a simple model of the magnetosheath. The results agree with the observed values of the ISEE satellite data within experimental uncertainties.
Simulation of financial market via nonlinear Ising model
NASA Astrophysics Data System (ADS)
Ko, Bonggyun; Song, Jae Wook; Chang, Woojin
2016-09-01
In this research, we propose a practical method for simulating the financial return series whose distribution has a specific heaviness. We employ the Ising model for generating financial return series to be analogous to those of the real series. The similarity between real financial return series and simulated one is statistically verified based on their stylized facts including the power law behavior of tail distribution. We also suggest the scheme for setting the parameters in order to simulate the financial return series with specific tail behavior. The simulation method introduced in this paper is expected to be applied to the other financial products whose price return distribution is fat-tailed.
Ising-like models on arbitrary graphs: The Hadamard way
NASA Astrophysics Data System (ADS)
Mosseri, Rémy
2015-01-01
We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect that the existence of a fast Hadamard transform algorithm (used, for instance, in image compression processes), together with the sparseness of the coding vector, may provide ways to fasten the spectrum computation. Applying this formalism to regular graphs, such as hypercubic graphs, we obtain a simple recurrence relation for the spectrum, which significantly speeds up its determination. First attempts to analyze partition functions and transfer matrices are also presented.
Oscillating hysteresis in the q -neighbor Ising model
NASA Astrophysics Data System (ADS)
JÈ©drzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q ≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q . Moreover, we show that for q =3 the phase transition is continuous and that it is discontinuous for larger values of q . For q >3 , the hysteresis exhibits oscillatory behavior—expanding for even values of q and shrinking for odd values of q . Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q =5 , which might be taken as evidence for the so-called mixed-order phase transition.
Oscillating hysteresis in the q-neighbor Ising model.
Jȩdrzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q. Moreover, we show that for q=3 the phase transition is continuous and that it is discontinuous for larger values of q. For q>3, the hysteresis exhibits oscillatory behavior-expanding for even values of q and shrinking for odd values of q. Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q=5, which might be taken as evidence for the so-called mixed-order phase transition. PMID:26651645
Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
Dusuel, Sebastien; Kamfor, Michael; Schmidt, Kai Phillip; Thomale, Ronny; Vidal, Julien
2010-02-01
We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.
Phase diagram and critical behavior of the antiferromagnetic Ising model in an external field
NASA Astrophysics Data System (ADS)
Jeferson Lourenço, Bruno; Dickman, Ronald
2016-03-01
We study the critical properties of the antiferromagnetic spin-1/2 Ising model in an external field on the square lattice. Using tomographic entropic sampling, a flat-histogram simulation method, we estimate the number of configurations, Ω , and related microcanonical averages in the energy-magnetization space, for system sizes L = 10-30. The critical line and exponents are calculated using finite-size scaling analysis in the temperature-external field plane. With these estimates in hand, we perform detailed studies of critical behavior using Metropolis sampling of larger systems (L≤slant 320 ). These results are compared to several approximate theoretical methods. Our estimates of critical exponents and Binder’s reduced fourth cumulant along the critical line are in very good agreement with their respective literature values for the two-dimensional Ising universality class. We verify as well that the specific heat scales ˜ \\ln L along the critical line, as expected for an Ising-like critical point.
The Ising Model Applied on Chronification of Pain
2016-01-01
This is a hypothesis-article suggesting an entirely new framework for understanding and treating longstanding pain. Most medical and psychological models are described with boxes and arrows. Such models are of little clinical and explanatory use when describing the phenomenon of chronification of pain due to unknown causes. To date no models that have been provided - and tested in a scientific satisfactory way - lays out a plan for specific assessment due to a specific causal explanation, and in the end serves the clinicians, patients and researcher with tools on how to address the specific pain condition to every individual pain patient's condition. By applying the Ising model (from physics) on the phenomenon of chronification of pain, one is able to detangle all these factors, and thus have a model that both suggests an explanation of the condition and outlines how one might target the treatment of chronic pain patients with the use of network science. PMID:26398917
From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction
NASA Astrophysics Data System (ADS)
de Tilière, Béatrice
2013-04-01
Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph G and the dimer model defined on a decorated version {{G}} of this graph (Fisher in J Math Phys 7:1776-1781, 1966). In this paper we explicitly relate the dimer model associated to the critical Ising model and critical cycle rooted spanning forests (CRSFs). This relation is established through characteristic polynomials, whose definition only depends on the respective fundamental domains, and which encode the combinatorics of the model. We first show a matrix-tree type theorem establishing that the dimer characteristic polynomial counts CRSFs of the decorated fundamental domain {{G}_1}. Our main result consists in explicitly constructing CRSFs of {{G}_1} counted by the dimer characteristic polynomial, from CRSFs of G 1, where edges are assigned Kenyon's critical weight function (Kenyon in Invent Math 150(2):409-439, 2002); thus proving a relation on the level of configurations between two well known 2-dimensional critical models.
Saturation field entropies of antiferromagnetic Ising models: Ladders and the kagome lattice
NASA Astrophysics Data System (ADS)
Varma, Vipin Kerala
2013-10-01
Saturation field entropies of antiferromagnetic Ising models on quasi-one-dimensional lattices (ladders) and the kagome lattice are calculated. The former is evaluated exactly by constructing the corresponding transfer matrices, while the latter calculation uses Binder's algorithm for efficiently and exactly computing the partition function of over 1300 spins to give Skag/kB=0.393589(6). We comment on the relation of the kagome lattice to the experimental situation in the spin-ice compound Dy2Ti2O7.
Three-spin interaction Ising model with a nondegenerate ground state at zero applied field
NASA Astrophysics Data System (ADS)
Bidaux, R.; Boccara, N.; Forgàcs, G.
1986-10-01
The field-temperature phase diagram of a two-dimensional, three-spin interaction Ising model is studied using two different methods: mean field approximation and numerical transfer matrix techniques. The former leads to a rather rich phase diagram in which two separate phases with different symmetries can be found, and which presents first-order transition lines, a triple point, and a critical end point, like the solid-liquid-gas phase diagram of a pure compound. The numerical transfer matrix study confirms part of these results, but does not clearly evidence the existence of the less symmetric phase.
Quantum cluster algorithm for frustrated Ising models in a transverse field
NASA Astrophysics Data System (ADS)
Biswas, Sounak; Rakala, Geet; Damle, Kedar
2016-06-01
Working within the stochastic series expansion framework, we introduce and characterize a plaquette-based quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a demonstration of the capabilities of this algorithm, we show that a relatively small ferromagnetic next-nearest-neighbor coupling drives the transverse field Ising antiferromagnet on the triangular lattice from an antiferromagnetic three-sublattice ordered state at low temperature to a ferrimagnetic three-sublattice ordered state.
Planar ordering in the plaquette-only gonihedric Ising model
NASA Astrophysics Data System (ADS)
Mueller, Marco; Janke, Wolfhard; Johnston, Desmond A.
2015-05-01
In this paper we conduct a careful multicanonical simulation of the isotropic 3d plaquette ("gonihedric") Ising model and confirm that a planar, fuki-nuke type order characterises the low-temperature phase of the model. From consideration of the anisotropic limit of the model we define a class of order parameters which can distinguish the low- and high-temperature phases in both the anisotropic and isotropic cases. We also verify the recently voiced suspicion that the order parameter like behaviour of the standard magnetic susceptibility χm seen in previous Metropolis simulations was an artefact of the algorithm failing to explore the phase space of the macroscopically degenerate low-temperature phase. χm is therefore not a suitable order parameter for the model.
Emergent Ising degrees of freedom in the J1-J2-J3 model for the iron tellurides
NASA Astrophysics Data System (ADS)
Zhang, Guanghua; Fernandes, Rafael; Flint, Rebecca
The iron-telluride family of superconductors form a double-stripe [ Q = (π / 2 , π / 2) ] magnetic order, which can be captured within a J1 -J2 -J3 Heisenberg model in the regime J3 >>J2 >>J1 . Intriguingly, besides breaking spin-rotational symmetry, the ground state manifold has three additional Ising degrees of freedom. Via their coupling to the lattice, they give rise to a monoclinic distortion and to two non-uniform lattice distortions with wave-vector (π , π) . Because the ground state is four-fold degenerate (mod rotations in spin space), only two of these Ising order parameters are independent. Here we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order. All three transitions (corresponding to the condensations of two Ising and one magnetic order parameter) are simultaneous and first order in three dimensions, but lower dimensionality (or equivalently weaker interlayer coupling) and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions.
Reentrance of disorder in the anisotropic shuriken Ising model
NASA Astrophysics Data System (ADS)
Pohle, Rico; Benton, Owen; Jaubert, L. D. C.
2016-07-01
Frustration is often a key ingredient for reentrance mechanisms. Here we study the frustrated anisotropic shuriken Ising model, where it is possible to extend the notion of reentrance between disordered phases, i.e., in absence of phase transitions. By tuning the anisotropy of the lattice, we open a window in the phase diagram where magnetic disorder prevails down to zero temperature, in a classical analogy with a quantum critical point. In this region, the competition between multiple disordered ground states gives rise to a double crossover where both the low- and high-temperature regimes are less correlated than the intervening classical spin liquid. This reentrance of disorder is characterized by an entropy plateau and a multistep Curie law crossover. Our theory is developed based on Monte Carlo simulations, analytical Husimi-tree calculations and an exact decoration-iteration transformation. Its relevance to experiments, in particular, artificial lattices, is discussed.
Driven-dissipative Ising model: Mean-field solution
NASA Astrophysics Data System (ADS)
Goldstein, G.; Aron, C.; Chamon, C.
2015-11-01
We study the fate of the Ising model and its universal properties when driven by a rapid periodic drive and weakly coupled to a bath at equilibrium. The far-from-equilibrium steady-state regime is accessed by means of a Floquet mean-field approach. We show that, depending on the details of the bath, the drive can strongly renormalize the critical temperature to higher temperatures, modify the critical exponents, or even change the nature of the phase transition from second to first order after the emergence of a tricritical point. Moreover, by judiciously selecting the frequency of the field and by engineering the spectrum of the bath, one can drive a ferromagnetic Hamiltonian to an antiferromagnetically ordered phase and vice versa.
Robust criticality of an Ising model on rewired directed networks
NASA Astrophysics Data System (ADS)
Lipowski, Adam; Gontarek, Krzysztof; Lipowska, Dorota
2015-06-01
We show that preferential rewiring, which is supposed to mimic the behavior of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behavior. For the nonrewired random graph version, due to a constant number of out-links for each site, we write a simple mean-field-like equation describing the behavior of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behavior is traced back to the formation of a relatively small core of agents that influence the entire system.
Modulated phases and chaotic behavior in a spin-1 Ising model with competing interactions
NASA Astrophysics Data System (ADS)
Tomé, Tânia; Salinas, S. R.
1989-02-01
We formulate the Blume-Capel spin-1 Ising model, with competing first- and second-neighbor interactions along the branches of a Cayley tree, in the infinite-coordination limit, as a discrete two-dimensional nonlinear mapping problem. The phase diagram displays multicritical points and many modulated phases. Mean-field calculations for the analogous model on a cubic lattice give the same qualitative results. We take advantage of the simplicity of the mapping to show the existence of complete devil's staircases, at low temperatures T, with increasing values of the Hausdorff dimensionality DF with T. We show that there are regions of the phase diagram associated with positive values of the Lyapunov exponents of the mapping, and we give strong numerical evidence to support the existence of a strange attractor with a Lyapunov dimension Dλ>1. We also find a route to chaos, according to the scenario of Feigenbaum, with a reasonable estimate of the exponent δ.
Phase Transitions for Quantum Markov Chains Associated with Ising Type Models on a Cayley Tree
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Barhoumi, Abdessatar; Souissi, Abdessatar
2016-05-01
The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing interactions on a Cayley tree of order two. By the phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. We also study some algebraic property of the disordered phase of the model, which is a new phenomena even in a classical setting.
Neutron diffraction study on the two-dimensional Ising system KEr(MoO{sub 4}){sub 2}
Mat'as, Slavomir; Dudzik, Esther; Feyerherm, Ralf; Gerischer, Sebastian; Klemke, Sebastian; Prokes, Karel; Orendacova, Alzbeta
2010-11-01
The magnetic properties of the two-dimensional Ising antiferromagnet KEr(MoO{sub 4}){sub 2} have been investigated below and above transition temperature T{sub N}{approx}0.95 K in zero field and in fields up to 6.5 T by means of elastic neutron-diffraction, heat-capacity, and magnetization measurements. The low-temperature signal recorded at 0.34 K by neutron diffraction is explained within a noncollinear magnetic structure model. However, additional contribution is also present when applying the external magnetic field along the c axis even at temperatures well above the magnetic transition temperature T{sub N}. Various explanations are discussed.
Amoruso, C.; Moore, M. A.; Hartmann, A. K.; Hastings, M. B.
2006-12-31
We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with {kappa}{approx_equal}2.1. An argument is given that their fractal dimension d{sub f} is related to their interface energy exponent {theta} by d{sub f}-1=3/[4(3+{theta})], which is consistent with the commonly quoted values d{sub f}{approx_equal}1.27 and {theta}{approx_equal}-0.28.
A simulation of the mixed spin 3-spin 3/2 ferrimagnetic Ising model
NASA Astrophysics Data System (ADS)
Özkan, Aycan
2016-01-01
The mixed spin 3-spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals -4 ≤ DA/J ≤ 8 and -4 ≤ DB/J ≤ 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through DA/J = 2 at kT/J = 0. The values of the critical exponents (ν, α , β and γ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected DA/J values (-2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model (ν = 1, α = α‧ = 0, β = 0.125, β‧ = 0.875 and γ = γ‧ = 1.75).
Differential geometry of the space of Ising models
NASA Astrophysics Data System (ADS)
Machta, Benjamin; Chachra, Ricky; Transtrum, Mark; Sethna, James
2012-02-01
We use information geometry to understand the emergence of simple effective theories, using an Ising model perturbed with terms coupling non-nearest-neighbor spins as an example. The Fisher information is a natural metric of distinguishability for a parameterized space of probability distributions, applicable to models in statistical physics. Near critical points both the metric components (four-point susceptibilities) and the scalar curvature diverge with corresponding critical exponents. However, connections to Renormalization Group (RG) ideas have remained elusive. Here, rather than looking at RG flows of parameters, we consider the reparameterization-invariant flow of the manifold itself. To do this we numerically calculate the metric in the original parameters, taking care to use only information available after coarse-graining. We show that under coarse-graining the metric contracts very anisotropically, leading to a ``sloppy'' spectrum with the metric's Eigenvalues spanning many orders of magnitude. Our results give a qualitative explanation for the success of simple models: most directions in parameter space become fundamentally indistinguishable after coarse-graining.
Modeling Dark Energy Through AN Ising Fluid with Network Interactions
NASA Astrophysics Data System (ADS)
Luongo, Orlando; Tommasini, Damiano
2014-12-01
We show that the dark energy (DE) effects can be modeled by using an Ising perfect fluid with network interactions, whose low redshift equation of state (EoS), i.e. ω0, becomes ω0 = -1 as in the ΛCDM model. In our picture, DE is characterized by a barotropic fluid on a lattice in the equilibrium configuration. Thus, mimicking the spin interaction by replacing the spin variable with an occupational number, the pressure naturally becomes negative. We find that the corresponding EoS mimics the effects of a variable DE term, whose limiting case reduces to the cosmological constant Λ. This permits us to avoid the introduction of a vacuum energy as DE source by hand, alleviating the coincidence and fine tuning problems. We find fairly good cosmological constraints, by performing three tests with supernovae Ia (SNeIa), baryonic acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements. Finally, we perform the Akaike information criterion (AIC) and Bayesian information criterion (BIC) selection criteria, showing that our model is statistically favored with respect to the Chevallier-Polarsky-Linder (CPL) parametrization.
Universal Finite Size Corrections and the Central Charge in Non-solvable Ising Models
NASA Astrophysics Data System (ADS)
Giuliani, Alessandro; Mastropietro, Vieri
2013-11-01
We investigate a non-solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength λ. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all and λ 0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.
NASA Astrophysics Data System (ADS)
Ehrmann, Andrea; Blachowicz, Tomasz; Zghidi, Hafed
2015-05-01
Modelling hysteresis behaviour, as it can be found in a broad variety of dynamical systems, can be performed in different ways. An elementary approach, applied for a set of elementary cells, which uses only two possible states per cell, is the Ising model. While such Ising models allow for a simulation of many systems with sufficient accuracy, they nevertheless depict some typical features which must be taken into account with proper care, such as meta-stability or the externally applied field sweeping speed. This paper gives a general overview of recent results from Ising models from the perspective of a didactic model, based on a 2D spreadsheet analysis, which can be used also for solving general scientific problems where direct next-neighbour interactions take place.
Optimal control in nonequilibrium systems: Dynamic Riemannian geometry of the Ising model
NASA Astrophysics Data System (ADS)
Rotskoff, Grant M.; Crooks, Gavin E.
2015-12-01
A general understanding of optimal control in nonequilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear response protocol is endowed with a Riemannian metric related to generalized susceptibilities, and that geodesics on this manifold are the nonequilibrium control protocols with the lowest achievable dissipation. While this elegant mathematical framework has inspired numerous studies of exactly solvable systems, no description of the thermodynamic geometry yet exists when the metric cannot be derived analytically. Herein, we numerically construct the dynamic metric of the two-dimensional Ising model in order to study optimal protocols for reversing the net magnetization.
Form factor expansions in the 2D Ising model and Painlevé VI
NASA Astrophysics Data System (ADS)
Mangazeev, Vladimir V.; Guttmann, Anthony J.
2010-10-01
We derive a Toda-type recurrence relation, in both high- and low-temperature regimes, for the λ-extended diagonal correlation functions C(N,N;λ) of the two-dimensional Ising model, using an earlier connection between diagonal form factor expansions and tau-functions within Painlevé VI (PVI) theory, originally discovered by Jimbo and Miwa. This greatly simplifies the calculation of the diagonal correlation functions, particularly their λ-extended counterparts. We also conjecture a closed form expression for the simplest off-diagonal case C(0,1;λ) where a connection to PVI theory is not known. Combined with the results for diagonal correlations these give all the initial conditions required for the λ-extended version of quadratic difference equations for the correlation functions discovered by McCoy, Perk and Wu. The results obtained here should provide a further potential algorithmic improvement in the λ-extended case, and facilitate other developments.
±J Ising model on homogeneous Archimedean lattices
NASA Astrophysics Data System (ADS)
Valdés, J. F.; Lebrecht, W.; Vogel, E. E.
2012-04-01
We tackle the problem of finding analytical expressions describing the ground state properties of homogeneous Archimedean lattices over which a generalized Edwards-Anderson model (±J Ising model) is defined. A local frustration analysis is performed based on representative cells for square lattices, triangular lattices and honeycomb lattices. The concentration of ferromagnetic (F) bonds x is used as the independent variable in the analysis (1-x is the concentration for antiferromagnetic (A) bonds), where x spans the range [0.0,1.0]. The presence of A bonds brings frustration, whose clear manifestation is when bonds around the minimum possible circuit of bonds (plaquette) cannot be simultaneously satisfied. The distribution of curved (frustrated) plaquettes within the representative cell is determinant for the evaluation of the parameters of interest such as average frustration segment, energy per bond, and fractional content of unfrustrated bonds. Two methods are developed to cope with this analysis: one based on the direct probability of a plaquette being curved; the other one is based on the consideration of the different ways bonds contribute to the particular plaquette configuration. Exact numerical simulations on a large number of randomly generated samples allow to validate previously described theoretical analysis. It is found that the second method presents slight advantages over the first one. However, both methods give an excellent description for most of the range for x. The small deviations at specific intervals of x for each lattice have to do with the self-imposed limitations of both methods due to practical reasons. A particular discussion for the point x=0.5 for each one of the lattices also shines light on the general trends of the properties described here.
Hyperinflation in the Ising model on quasiperiodic chains
NASA Astrophysics Data System (ADS)
Odagaki, T.
1990-02-01
Using a hyperinflation rule, the free energy of the two component Ising system on a chain with an arbitrary quasiperiodic order is shown to be given by an average of the free energy of each component, in agreement with the result obtained by the transfer matrix formalism.
Ising model of cardiac thin filament activation with nearest-neighbor cooperative interactions
NASA Technical Reports Server (NTRS)
Rice, John Jeremy; Stolovitzky, Gustavo; Tu, Yuhai; de Tombe, Pieter P.; Bers, D. M. (Principal Investigator)
2003-01-01
We have developed a model of cardiac thin filament activation using an Ising model approach from equilibrium statistical physics. This model explicitly represents nearest-neighbor interactions between 26 troponin/tropomyosin units along a one-dimensional array that represents the cardiac thin filament. With transition rates chosen to match experimental data, the results show that the resulting force-pCa (F-pCa) relations are similar to Hill functions with asymmetries, as seen in experimental data. Specifically, Hill plots showing (log(F/(1-F)) vs. log [Ca]) reveal a steeper slope below the half activation point (Ca(50)) compared with above. Parameter variation studies show interplay of parameters that affect the apparent cooperativity and asymmetry in the F-pCa relations. The model also predicts that Ca binding is uncooperative for low [Ca], becomes steeper near Ca(50), and becomes uncooperative again at higher [Ca]. The steepness near Ca(50) mirrors the steep F-pCa as a result of thermodynamic considerations. The model also predicts that the correlation between troponin/tropomyosin units along the one-dimensional array quickly decays at high and low [Ca], but near Ca(50), high correlation occurs across the whole array. This work provides a simple model that can account for the steepness and shape of F-pCa relations that other models fail to reproduce.
NASA Astrophysics Data System (ADS)
Thomaz, M. T.; Corrêa Silva, E. V.
2016-03-01
We derive the exact Helmholtz free energy (HFE) of the standard and staggered one-dimensional Blume-Emery-Griffiths (BEG) model in the presence of an external longitudinal magnetic field. We discuss in detail the thermodynamic behavior of the ferromagnetic version of the model, which exhibits magnetic field-dependent plateaux in the z-component of its magnetization at low temperatures. We also study the behavior of its specific heat and entropy, both per site, at finite temperature. The degeneracy of the ground state, at T=0, along the lines that separate distinct phases in the phase diagram of the ferromagnetic BEG model is calculated, extending the study of the phase diagram of the spin-1 antiferromagnetic (AF) Ising model in S.M. de Souza and M.T. Thomaz, J. Magn. and Magn. Mater. 354 (2014) 205 [5]. We explore the implications of the equality of phase diagrams, at T=0, of the ferromagnetic BEG model with K/|J| = - 2 and of the spin-1 AF Ising model for D/|J| > 1/2.
Exact algorithm for sampling the two-dimensional Ising spin glass.
Thomas, Creighton K; Middleton, A Alan
2009-10-01
A sampling algorithm is presented that generates spin-glass configurations of the two-dimensional Edwards-Anderson Ising spin glass at finite temperature with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow dynamics of direct simulation and can be used to study long-range correlation functions and coarse-grained dynamics. The algorithm uses a correspondence between spin configurations on a regular lattice and dimer (edge) coverings of a related graph: Wilson's algorithm [D. B. Wilson, Proceedings of the Eighth Symposium on Discrete Algorithms (SIAM, Philadelphia, 1997), p 258] for sampling dimer coverings on a planar lattice is adapted to generate samplings for the dimer problem corresponding to both planar and toroidal spin-glass samples. This algorithm is recursive: it computes probabilities for spins along a "separator" that divides the sample in half. Given the spins on the separator, sample configurations for the two separated halves are generated by further division and assignment. The algorithm is simplified by using Pfaffian elimination rather than Gaussian elimination for sampling dimer configurations. For n spins and given floating point precision, the algorithm has an asymptotic run-time of O(n(3/2)); it is found that the required precision scales as inverse temperature and grows only slowly with system size. Sample applications and benchmarking results are presented for samples of size up to n=128(2), with fixed and periodic boundary conditions. PMID:19905483
NASA Astrophysics Data System (ADS)
Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas
2016-06-01
By performing a high-statistics simulation of the D =4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.
Exact solution of the spin-1/2 Ising model on the Shastry Sutherland (orthogonal-dimer) lattice
NASA Astrophysics Data System (ADS)
Strečka, Jozef
2006-01-01
A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4 8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lattices.
NASA Astrophysics Data System (ADS)
Lopes Cardozo, David; Holdsworth, Peter C. W.
2016-04-01
The magnetization probability density in d = 2 and 3 dimensional Ising models in slab geometry of volume L\\paralleld-1× {{L}\\bot} is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field. The finite-size scaling of this distribution and its dependence on the system aspect-ratio ρ =\\frac{{{L}\\bot}}{{{L}\\parallel}} and boundary conditions are discussed. In the limiting case ρ \\to 0 of a macroscopically large slab ({{L}\\parallel}\\gg {{L}\\bot} ) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.
Physics and financial economics (1776-2014): puzzles, Ising and agent-based models.
Sornette, Didier
2014-06-01
This short review presents a selected history of the mutual fertilization between physics and economics--from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the 'Emerging Intelligence Market Hypothesis' to reconcile the pervasive presence of 'noise traders' with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets. PMID:24875470
Physics and financial economics (1776-2014): puzzles, Ising and agent-based models
NASA Astrophysics Data System (ADS)
Sornette, Didier
2014-06-01
This short review presents a selected history of the mutual fertilization between physics and economics—from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the ‘Emerging Intelligence Market Hypothesis’ to reconcile the pervasive presence of ‘noise traders’ with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.
Canonical vs. micro-canonical sampling methods in a 2D Ising model
Kepner, J.
1990-12-01
Canonical and micro-canonical Monte Carlo algorithms were implemented on a 2D Ising model. Expressions for the internal energy, U, inverse temperature, Z, and specific heat, C, are given. These quantities were calculated over a range of temperature, lattice sizes, and time steps. Both algorithms accurately simulate the Ising model. To obtain greater than three decimal accuracy from the micro-canonical method requires that the more complicated expression for Z be used. The overall difference between the algorithms is small. The physics of the problem under study should be the deciding factor in determining which algorithm to use. 13 refs., 6 figs., 2 tabs.
Self-Organizing Two-Temperature Ising Model Describing Human Segregation
NASA Astrophysics Data System (ADS)
Ódor, Géza
A two-temperature Ising-Schelling model is introduced and studied for describing human segregation. The self-organized Ising model with Glauber kinetics simulated by Müller et al. exhibits a phase transition between segregated and mixed phases mimicking the change of tolerance (local temperature) of individuals. The effect of external noise is considered here as a second temperature added to the decision of individuals who consider a change of accommodation. A numerical evidence is presented for a discontinuous phase transition of the magnetization.
Relations between short-range and long-range Ising models.
Angelini, Maria Chiara; Parisi, Giorgio; Ricci-Tersenghi, Federico
2014-06-01
We perform a numerical study of the long-range (LR) ferromagnetic Ising model with power law decaying interactions (J∝r{-d-σ}) on both a one-dimensional chain (d=1) and a square lattice (d=2). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters (d,σ) to that of a short-range (SR) model in an equivalent dimension D. We then study the critical behavior of the d=2 LR model close to the lower critical σ, uncovering that the spatial correlation function decays with two different power laws: The effect of the subdominant power law is much stronger than finite-size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak [Phys. Rev. B 8, 281 (1973)], thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco [arXiv:1207.1018] of having a new set of RG fixed points in addition to the mean-field one and the SR one. PMID:25019738
Relations between short-range and long-range Ising models
NASA Astrophysics Data System (ADS)
Angelini, Maria Chiara; Parisi, Giorgio; Ricci-Tersenghi, Federico
2014-06-01
We perform a numerical study of the long-range (LR) ferromagnetic Ising model with power law decaying interactions (J ∝r-d-σ) on both a one-dimensional chain (d =1) and a square lattice (d =2). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters (d,σ) to that of a short-range (SR) model in an equivalent dimension D. We then study the critical behavior of the d =2 LR model close to the lower critical σ, uncovering that the spatial correlation function decays with two different power laws: The effect of the subdominant power law is much stronger than finite-size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak [Phys. Rev. B 8, 281 (1973), 10.1103/PhysRevB.8.281], thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco [arXiv:1207.1018] of having a new set of RG fixed points in addition to the mean-field one and the SR one.
NASA Astrophysics Data System (ADS)
Hasenbusch, Martin
2010-09-01
We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry-breaking boundary conditions. To this end we simulate the improved Blume-Capel model on the simple cubic lattice. We study the two cases ++ , where all spins at the boundary are fixed to +1 and +- , where the spins at one boundary are fixed to +1 while those at the other boundary are fixed to -1 . An important issue in analyzing Monte Carlo and experimental data are corrections to scaling. Since we simulate an improved model, leading corrections to scaling, which are proportional to L0-ω , where L0 is the thickness of the film and ω≈0.8 , can be ignored. This allows us to focus on corrections to scaling that are caused by the boundary conditions. The analysis of our data shows that these corrections can be accounted for by an effective thickness L0,eff=L0+Ls . Studying the correlation length of the films, the energy per area, the magnetization profile, and the thermodynamic Casimir force at the bulk critical point we find Ls=1.9(1) for our model and the boundary conditions discussed here. Using this result for Ls we find a nice collapse of the finite-size scaling curves obtained for the thicknesses L0=8.5 , 16.5, and 32.5 for the full range of temperatures that we consider. We compare our results for the finite-size scaling functions θ++ and θ+- of the thermodynamic Casimir force with those obtained in a previous Monte Carlo study, by the de Gennes-Fisher local-functional method, field theoretic methods, and an experiment with a classical binary liquid mixture.
The Finite-Size Scaling Study of the Ising Model for the Fractals
NASA Astrophysics Data System (ADS)
Merdan, Z.; Bayirli, M.; Günen, A.; Bülbül, M.
2016-04-01
The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and df^{β } =1.876(8), df^{γ } =3.747(10), df^{α } =2.081(68), df^{δ } =1.940(22), df^{η } =2.178(10), df^{ν } =2.960(22), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and df^{β } =1.875, df^{γ } =3.75, df^{α } =2, df^{δ } =1.933, df^{η } =2.25, df^{ν } =3.
Spontaneous magnetization of the Ising model on the union jack and 4-6 lattices
NASA Astrophysics Data System (ADS)
Lin, K. Y.; Wang, S. C.
1988-03-01
Spontaneous magnetization of the Ising model on the anisotropic Union Jack and 4-6 lattices are derived exactly. The conjecture by Lin and Wang is confirmed. Our result is a generalization of the recent work on the isotropic Union Jack lattice by Choy and Baxter.
Spontaneous magnetization of the Ising model on a 4-8 lattice
NASA Astrophysics Data System (ADS)
Lin, K. Y.
1988-03-01
Spontaneous magnetization of the Ising model on a 4-8 lattice is derived. The result agrees with the conjecture of Lin, Kao and Chen. Our derivation is closely related to the recent work of Choy and Baxter on the isotropic Union Jack lattice.
ADDENDUM: Addendum to `On the singularity structure of the 2D Ising model susceptibility'
NASA Astrophysics Data System (ADS)
Nickel, Bernie
2000-03-01
A remarkable product formula first derived by Palmer and Tracy (1981 Adv. Appl. Math. 2 329) for the integrand of the two-dimensional Ising model susceptibility expansion coefficients icons/Journals/Common/chi" ALT="chi" ALIGN="TOP"/> (2n ) for temperatures T less than the critical T c is shown to apply equally for icons/Journals/Common/chi" ALT="chi" ALIGN="TOP"/> (2n +1) for T >T c and agrees with formulae derived by Yamada (1984 Prog. Theor. Phys. 71 1416). This new representation simplifies the derivation of the results in the original paper of this title (1999 J. Phys. A: Math. Gen. 32 3889) to the extent that the leading series behaviour and the singularity structure can be deduced almost by inspection. The derivation of series is also simplified and I show, using extended series and knowledge of the singularity structure, that there is now unambiguous evidence for correction to scaling terms in the susceptibility beyond those inferred from a nonlinear scaling field analysis.
An analysis of intergroup rivalry using Ising model and reinforcement learning
NASA Astrophysics Data System (ADS)
Zhao, Feng-Fei; Qin, Zheng; Shao, Zhuo
2014-01-01
Modeling of intergroup rivalry can help us better understand economic competitions, political elections and other similar activities. The result of intergroup rivalry depends on the co-evolution of individual behavior within one group and the impact from the rival group. In this paper, we model the rivalry behavior using Ising model. Different from other simulation studies using Ising model, the evolution rules of each individual in our model are not static, but have the ability to learn from historical experience using reinforcement learning technique, which makes the simulation more close to real human behavior. We studied the phase transition in intergroup rivalry and focused on the impact of the degree of social freedom, the personality of group members and the social experience of individuals. The results of computer simulation show that a society with a low degree of social freedom and highly educated, experienced individuals is more likely to be one-sided in intergroup rivalry.
Magnetization plateaus and phase diagrams of the Ising model on the Shastry-Sutherland lattice
NASA Astrophysics Data System (ADS)
Deviren, Seyma Akkaya
2015-11-01
The magnetization properties of a two-dimensional spin-1/2 Ising model on the Shastry-Sutherland lattice are studied within the effective-field theory (EFT) with correlations. The thermal behavior of the magnetizations is investigated in order to characterize the nature (the first- or second-order) of the phase transitions as well as to obtain the phase diagrams of the model. The internal energy, specific heat, entropy and free energy of the system are also examined numerically as a function of the temperature in order to confirm the stability of the phase transitions. The applied field dependence of the magnetizations is also examined to find the existence of the magnetization plateaus. For strong enough magnetic fields, several magnetization plateaus are observed, e.g., at 1/9, 1/8, 1/3 and 1/2 of the saturation. The phase diagrams of the model are constructed in two different planes, namely (h/|J|, |J‧|/|J|) and (h/|J|, T/|J|) planes. It was found that the model exhibits first- and second-order phase transitions; hence tricitical point is also observed in additional to the zero-temperature critical point. Moreover the Néel order (N), collinear order (C) and ferromagnetic (F) phases are also found with appropriate values of the system parameters. The reentrant behavior is also obtained whenever model displays two Néel temperatures. These results are compared with some theoretical and experimental works and a good overall agreement has been obtained.
Aspelmeier, T; Wang, Wenlong; Moore, M A; Katzgraber, Helmut G
2016-08-01
The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems. PMID:27627255
NASA Astrophysics Data System (ADS)
Aspelmeier, T.; Wang, Wenlong; Moore, M. A.; Katzgraber, Helmut G.
2016-08-01
The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.
Graphical Representations for Ising and Potts Models in General External Fields
NASA Astrophysics Data System (ADS)
Cioletti, Leandro; Vila, Roberto
2016-01-01
This work is concerned with the theory of graphical representation for the Ising and Potts models over general lattices with non-translation invariant external field. We explicitly describe in terms of the random-cluster representation the distribution function and, consequently, the expected value of a single spin for the Ising and q-state Potts models with general external fields. We also consider the Gibbs states for the Edwards-Sokal representation of the Potts model with non-translation invariant magnetic field and prove a version of the FKG inequality for the so called general random-cluster model (GRC model) with free and wired boundary conditions in the non-translation invariant case. Adding the amenability hypothesis on the lattice, we obtain the uniqueness of the infinite connected component and the almost sure quasilocality of the Gibbs measures for the GRC model with such general magnetic fields. As a final application of the theory developed, we show the uniqueness of the Gibbs measures for the ferromagnetic Ising model with a positive power-law decay magnetic field with small enough power, as conjectured in Bissacot et al. (Commun Math Phys 337: 41-53, 2015).
A universal form of slow dynamics in zero-temperature random-field Ising model
NASA Astrophysics Data System (ADS)
Ohta, H.; Sasa, S.
2010-04-01
The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial condition, we derive exactly an evolution equation for an order parameter. Through a bifurcation analysis of the obtained equation, we reveal a new class of cooperative slow dynamics with the determination of critical exponents.
NASA Astrophysics Data System (ADS)
Decelle, Aurélien; Ricci-Tersenghi, Federico
2014-02-01
In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the ℓ1 regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM.
Universal critical behavior of the two-dimensional Ising spin glass
NASA Astrophysics Data System (ADS)
Fernandez, L. A.; Marinari, E.; Martin-Mayor, V.; Parisi, G.; Ruiz-Lorenzo, J. J.
2016-07-01
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.
NASA Technical Reports Server (NTRS)
Spjeldvik, W. N.; Fritz, T. A.
1981-01-01
A description of energetic ion and electron behavior in the geomagnetic plasma sheet boundary layer is presented based on observations made by the medium-energy particle experiment on board ISEE 1. Three-dimensional observations of ions of energies 24-2081 keV and electrons of energies 22.5-1200 keV were obtained by the NOAA/WAPS instrument near the center of the magnetotail at a distance of approximately 15 earth radii. Large-scale motions of plasma sheet energetic particles are observed as an apparent result of a series of magnetospheric disturbances (substorms), which are characterized by substantial contractions and expansions. Ion flow velocity in a distinct boundary layer in energetic ions has been found to be in the earthward direction in each of the five ISEE 1 boundary crossings. Boundary layer motion during one of these crossings is interpreted as large-amplitude boundary waves with periodicities of a few minutes superimposed on the general plasma sheet behavior associated with the substorm process.
Morris, C M; Valdés Aguilar, R; Ghosh, A; Koohpayeh, S M; Krizan, J; Cava, R J; Tchernyshyov, O; McQueen, T M; Armitage, N P
2014-04-01
Kink bound states in the one-dimensional ferromagnetic Ising chain compound CoNb2O6 have been studied using high-resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schrödinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near 2 times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states--two pairs of kinks on neighboring chains. PMID:24745454
NASA Astrophysics Data System (ADS)
Morris, C. M.; Valdés Aguilar, R.; Ghosh, A.; Koohpayeh, S. M.; Krizan, J.; Cava, R. J.; Tchernyshyov, O.; McQueen, T. M.; Armitage, N. P.
2014-04-01
Kink bound states in the one-dimensional ferromagnetic Ising chain compound CoNb2O6 have been studied using high-resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schrödinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near 2 times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states—two pairs of kinks on neighboring chains.
Magnetic and Ising quantum phase transitions in a model for isoelectronically tuned iron pnictides
NASA Astrophysics Data System (ADS)
Wu, Jianda; Si, Qimiao; Abrahams, Elihu
2016-03-01
Considerations of the observed bad-metal behavior in Fe-based superconductors led to an early proposal for quantum criticality induced by isoelectronic P for As doping in iron arsenides, which has since been experimentally confirmed. We study here an effective model for the isoelectronically tuned pnictides using a large-N approach. The model contains antiferromagnetic and Ising-nematic order parameters appropriate for J1-J2 exchange-coupled local moments on an Fe square lattice, and a damping caused by coupling to itinerant electrons. The zero-temperature magnetic and Ising transitions are concurrent and essentially continuous. The order-parameter jumps are very small, and are further reduced by the interplane coupling; consequently, quantum criticality occurs over a wide dynamical range. Our results reconcile recent seemingly contradictory experimental observations concerning the quantum phase transition in the P-doped iron arsenides.
Smeared quantum phase transition in the dissipative random quantum Ising model
NASA Astrophysics Data System (ADS)
Vojta, Thomas; Hoyos, José A.
2010-01-01
We investigate the quantum phase transition in the random transverse-field Ising model under the influence of Ohmic dissipation. To this end, we numerically implement a strong-disorder renormalization-group scheme. We find that Ohmic dissipation destroys the quantum critical point and the associated quantum Griffiths phase by smearing. Our results quantitatively confirm a recent theory [J.A. Hoyos, T. Vojta, Phys. Rev. Lett. 100 (2008) 240601] of smeared quantum phase transitions.
Ising-like phase transition of an n-component Eulerian face-cubic model
NASA Astrophysics Data System (ADS)
Ding, Chengxiang; Guo, Wenan; Deng, Youjin
2013-11-01
By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the percolation of the complement of the Eulerian graph.
Form factors in the Bullough-Dodd-related models: The Ising model in a magnetic field
NASA Astrophysics Data System (ADS)
Alekseev, O. V.
2012-11-01
We consider a certain modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particle minimal form factors are eliminated from the construction. We consequently obtain a convenient representation for the multiparticle form factors, establish recurrence relations between them, and study their properties. We use the proposed construction to obtain the free-field representation of form factors for the lightest particles in the Φ 1,2 -perturbed minimal models. As an important example, we consider the Ising model in a magnetic field. We verify that the results obtained in the framework of the proposed free-field representation agree with the corresponding results obtained by solving the bootstrap equations.
Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field
NASA Astrophysics Data System (ADS)
Alekseev, O. V.
2012-04-01
A particular modification of the free-field representation of the form factors in the Bullough-Dodd model is considered. The two-particles minimal form factors are excluded from the construction. As a consequence, a convenient representation for the multiparticle form factors has been obtained, recurrence relations between them have been established, and their properties have been studied. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the Φ1, 2 perturbed minimal models. The Ising model in a magnetic field is considered as a significant example. The results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.
Inference of the sparse kinetic Ising model using the decimation method.
Decelle, Aurélien; Zhang, Pan
2015-05-01
In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014)] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ℓ(1)-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ℓ(1)-optimization-based methods. PMID:26066148
Evidence for two-dimensional Ising superconductivity in gated MoS₂.
Lu, J M; Zheliuk, O; Leermakers, I; Yuan, N F Q; Zeitler, U; Law, K T; Ye, J T
2015-12-11
The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field B(c2) far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced B(c2) is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field. PMID:26563134
Evidence for two-dimensional Ising superconductivity in gated MoS2
NASA Astrophysics Data System (ADS)
Lu, J. M.; Zheliuk, O.; Leermakers, I.; Yuan, N. F. Q.; Zeitler, U.; Law, K. T.; Ye, J. T.
2015-12-01
The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field Bc2 far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced Bc2 is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.
Ising spin network states for loop quantum gravity: a toy model for phase transitions
NASA Astrophysics Data System (ADS)
Feller, Alexandre; Livine, Etera R.
2016-03-01
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should emerge entirely from the correlations between the gravity fluctuations. In the context of loop quantum gravity, quantum states of geometry are defined as spin networks. These are graphs decorated with spin and intertwiners, which represent quantized excitations of areas and volumes of the space geometry. Here, we develop the condensed-matter point of view on extracting the physical and geometrical information from spin network states: we introduce new Ising spin network states, both in 2d on a square lattice and in 3d on a hexagonal lattice, whose correlations map onto the usual Ising model in statistical physics. We construct these states from the basic holonomy operators of loop gravity and derive a set of local Hamiltonian constraints that entirely characterize our states. We discuss their phase diagram and show how the distance can be reconstructed from the correlations in the various phases. Finally, we propose generalizations of these Ising states, which open the perspective to study the coarse-graining and dynamics of spin network states using well-known condensed-matter techniques and results.
Phase transition of p-adic Ising λ-model
Dogan, Mutlay; Akın, Hasan; Mukhamedov, Farrukh
2015-09-18
We consider an interaction of the nearest-neighbors and next nearest-neighbors for the mixed type p-adic λ-model with spin values (−1, +1) on a Cayley tree of order two. In the previous work we have proved the existence of the p-adic Gibbs measure for the model. In this work we have proved the existence of the phase transition occurs for the model.
Ising type models applied to Geophysics and high frequency market data
NASA Astrophysics Data System (ADS)
Mariani, M. C.; Bezdek, P.; Serpa, L.; Florescu, I.
2011-11-01
The classical Ising model was used to re-create the ferromagnetic phenomenon in statistical mechanics. The model describes the behavior of atoms in a lattice. Each atom may interact only with its neighbors, and has two states called spins. When the atoms polarize their spins, the resulting material exhibits a net magnetization. A similar model has been used before in financial math: the spins correspond to the buy/sell position of a trader and the polarization is equivalent with all the traders in the market wanting to sell. This leads to a market crash. In this work, we present extensions and applications to geophysics and high frequency market data.
ERIC Educational Resources Information Center
Singh, Satya Pal
2014-01-01
This paper presents a brief review of Ising's work done in 1925 for one dimensional spin chain with periodic boundary condition. Ising observed that no phase transition occurred at finite temperature in one dimension. He erroneously generalized his views in higher dimensions but that was not true. In 1941 Kramer and Wannier obtained…
NASA Astrophysics Data System (ADS)
Sornette, Didier; Zhou, Wei-Xing
2006-10-01
Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients, which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are overconfident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.
Monte Carlo Simulations of inter- and intra-grain spin structure of Ising and Heisenberg models
NASA Astrophysics Data System (ADS)
Leblanc, Martin
In order to keep supplying computer hard disk drives with more and more storage space, it is essential to have smaller bits. With smaller bits, superparamagnetism, the spontaneous flipping of the magnetic moments in a bit caused by thermal fluctuations, becomes increasingly important and impacts the stability of stored data. Recording media is composed of magnetic grains (usually made of CoCrPt alloys) roughly 10 nm in size from which bits are composed. Most modeling efforts that study magnetic recording media treat the grains as weakly interacting uniformly magnetized objects. In this work, the spin structure internal to a grain is examined along with the impact of varying the relative strengths of intrar-grain and inter-grain exchange interactions. The interplay between these two effects needs to be examined for a greater understanding of superparamagnetism as well as for the applications of the proposed Heat Assisted Magnetic Recording (HAMR) technology where thermal fluctuations facilitate head-field induced bit reversal in high anisotropy media. Simulations using the Monte Carlo method (with cluster-flipping algorithms) are performed on a 2D single-layer and multilayer Ising model with a strong intrar-grain exchange interaction J as well as a weak inter-grain exchange J'. A strong deviation from traditional behavior is found when J'/J is significant. M-H hysteresis loops are also calculated and the coercivity, H c is estimated. A large value represents a strong resilience to the superparamagnetic effect. It is found that taking into account the internal degrees of freedom has a significant effect on Hce. As the Ising model serves only as an approximation, preliminary simulations are also reported on a more realistic Heisenberg model with uniaxial anisotropy. Key Words: Ising model, Heisenberg model, Monte Carlo Simulation
Ultrafast vectorized multispin coding algorithm for the Monte Carlo simulation of the 3D Ising model
NASA Astrophysics Data System (ADS)
Wansleben, Stephan
1987-02-01
A new Monte Carlo algorithm for the 3D Ising model and its implementation on a CDC CYBER 205 is presented. This approach is applicable to lattices with sizes between 3·3·3 and 192·192·192 with periodic boundary conditions, and is adjustable to various kinetic models. It simulates a canonical ensemble at given temperature generating a new random number for each spin flip. For the Metropolis transition probability the speed is 27 ns per updates on a two-pipe CDC Cyber 205 with 2 million words physical memory, i.e. 1.35 times the cycle time per update or 38 million updates per second.
Ovchinnikov, O. S.; Jesse, S.; Kalinin, S. V.; Bintacchit, P.; Trolier-McKinstry, S.
2009-10-09
An approach for the direct identification of disorder type and strength in physical systems based on recognition analysis of hysteresis loop shape is developed. A large number of theoretical examples uniformly distributed in the parameter space of the system is generated and is decorrelated using principal component analysis (PCA). The PCA components are used to train a feed-forward neural network using the model parameters as targets. The trained network is used to analyze hysteresis loops for the investigated system. The approach is demonstrated using a 2D random-bond-random-field Ising model, and polarization switching in polycrystalline ferroelectric capacitors.
Geometrical aspects of critical Ising configurations in two dimensions
NASA Astrophysics Data System (ADS)
Blöte, H. W. J.; Knops, Y. M. M.; Nienhuis, B.
1992-06-01
We present a physical interpretation of a number of exotic exponents of the two-dimensional Ising model, i.e., exponents that do have a conformal classification, but outside the unitary grid. They describe the scaling behavior of geometric properties of Ising and random clusters. For instance, the probability that two spins at a distance r lie on the perimeter of the same Ising cluster decays as r-5/4 at criticality. These results are obtained via mappings on the Coulomb gas. A part of the Coulomb gas scenario is verified by means of finite-size scaling of transfer-matrix results.
LETTER TO THE EDITOR: Frustration in Ising-type spin models on the pyrochlore lattice
NASA Astrophysics Data System (ADS)
Bramwell, S. T.; Harris, M. J.
1998-04-01
We compare the behaviour of ferromagnetic and antiferromagnetic Ising-type spin models on the cubic pyrochlore lattice. With simple `up - down' Ising spins, the antiferromagnet is highly frustrated and the ferromagnet is not. However, such spin symmetry cannot be realized on the pyrochlore lattice, since it requires a unique symmetry axis, which is incompatible with the cubic symmetry. The only two-state spin symmetry which is compatible is that with four local 0953-8984/10/14/002/img5 anisotropy axes, which direct the spins to point in or out of the tetrahedral plaquettes of the pyrochlore lattice. We show how the local `in - out' magnetic anisotropy reverses the roles of the ferro- and antiferromagnetic exchange couplings with regard to frustration, such that the ferromagnet is highly frustrated and the antiferromagnet is not. The in - out ferromagnet is a magnetic analogue of the ice model, which we have termed the `spin ice model'. It is realized in the material 0953-8984/10/14/002/img6. The up - down antiferromagnet is also an analogue of the ice model, albeit a less direct one, as originally shown by Anderson. Combining these results shows that the up - down spin models map onto the in - out spin models with the opposite sign of the exchange coupling. We present Monte Carlo simulations of the susceptibility for each model, and discuss their relevance to experimental systems.
Supporting Kibble-Zurek Mechanism in Quantum Ising Model through a Trapped Ion
NASA Astrophysics Data System (ADS)
Hu, Changkang; Cui, Jinming; Huang, Yunfeng; Wang, Zhao; Cao, Dongyang; Wang, Jian; Lv, Weimin; Lu, Yong; Luo, Le; Campo, Adolfo; Han, Yongjian; Li, Chuanfeng; Guo, Guangcan
The Kibble-Zurek mechanism is the paradigm to account for the non adiabatic dynamics of a system across a phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. Our results support the Kibble-Zurek mechanism in the quantum regime and advance the quantum simulation of critical systems far-away from equilibrium.
Onsager and Kaufman's Calculation of the Spontaneous Magnetization of the Ising Model
NASA Astrophysics Data System (ADS)
Baxter, R. J.
2011-11-01
Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C.N. Yang published a derivation in Physical Review. In 1971 Onsager gave some clues to his and Kaufman's method, and there are copies of their correspondence in 1950 now available on the Web and elsewhere. Here we review how the calculation appears to have developed, and add a copy of a draft paper, almost certainly by Onsager and Kaufman, that obtains the result.
Condensation of helium in aerogel and athermal dynamics of the random-field Ising model.
Aubry, Geoffroy J; Bonnet, Fabien; Melich, Mathieu; Guyon, Laurent; Spathis, Panayotis; Despetis, Florence; Wolf, Pierre-Etienne
2014-08-22
High resolution measurements reveal that condensation isotherms of (4)He in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems. PMID:25192103
The Ising model for changes in word ordering rules in natural languages
NASA Astrophysics Data System (ADS)
Itoh, Yoshiaki; Ueda, Sumie
2004-11-01
The order of ‘noun and adposition’ is an important parameter of word ordering rules in the world’s languages. The seven parameters, ‘adverb and verb’ and others, depend strongly on the ‘noun and adposition’. Japanese as well as Korean, Tamil and several other languages seem to have a stable structure of word ordering rules, while Thai and other languages, which have the opposite word ordering rules to Japanese, are also stable in structure. It seems therefore that each language in the world fluctuates between these two structures like the Ising model for finite lattice.
Exact results for the site-dilute antiferromagnetic Ising model on finite triangular lattices
NASA Astrophysics Data System (ADS)
Farach, H. A.; Creswick, R. J.; Poole, C. P., Jr.
1988-04-01
Exact analytical and numerical results for the site-diluted antiferromagnetic Ising model on the triangular lattice (AFIT) are presented. For infinitesimal dilution the change in the free energy of the system is related to the distribution of local fields, and it is shown that for a frustrated system such as the AFIT, dilution lowers the entropy per spin. For lattices of finite size and dilution the transfer matrix for the partition function is evaluated numerically. The entropy per spin shows a marked minimum near a concentration of spins x=0.70, in some disagreement with earlier transfer-matrix results.
An Ising-like model for monolayer-monolayer coupling in lipid bilayers
NASA Astrophysics Data System (ADS)
Sornbundit, Kan; Modchang, Charin; Nuttavut, Narin; Ngamsaad, Waipot; Triampo, Darapond; Triampo, Wannapong
2013-07-01
We have proposed the Ising bilayer model to study the domain growth dynamics in lipid bilayers. Interactions within and between layers are adopted from recent experimental and theoretical data. We investigate the effects of the mismatch area on the domain coarsening dynamics in both symmetric and asymmetric lipid bilayers. To explore domain coarsening, we used the Monte Carlo (MC) method with a standard Kawasaki dynamics to simulate the systems. The results show that domains on both layers grow following a power-law and that the domains grow slower when the mismatch areas are increased.
Analysis of the phase transition for the Ising model on the frustrated square lattice
NASA Astrophysics Data System (ADS)
Kalz, Ansgar; Honecker, Andreas; Moliner, Marion
2011-11-01
We analyze the phase transition of the frustrated J1-J2 Ising model with antiferromagnetic nearest- and strong next-nearest-neighbor interactions on the square lattice. Using extensive Monte Carlo simulations we show that the nature of the phase transition for 1/2
The Ising model for prediction of disordered residues from protein sequence alone
NASA Astrophysics Data System (ADS)
Lobanov, Michail Yu; Galzitskaya, Oxana V.
2011-06-01
Intrinsically disordered regions serve as molecular recognition elements, which play an important role in the control of many cellular processes and signaling pathways. It is useful to be able to predict positions of disordered residues and disordered regions in protein chains using protein sequence alone. A new method (IsUnstruct) based on the Ising model for prediction of disordered residues from protein sequence alone has been developed. According to this model, each residue can be in one of two states: ordered or disordered. The model is an approximation of the Ising model in which the interaction term between neighbors has been replaced by a penalty for changing between states (the energy of border). The IsUnstruct has been compared with other available methods and found to perform well. The method correctly finds 77% of disordered residues as well as 87% of ordered residues in the CASP8 database, and 72% of disordered residues as well as 85% of ordered residues in the DisProt database.
Noncyclic geometric quantum computation and preservation of entanglement for a two-qubit Ising model
NASA Astrophysics Data System (ADS)
Rangani Jahromi, H.; Amniat-Talab, M.
2015-10-01
After presenting an exact analytical solution of time-dependent Schrödinger equation, we study the dynamics of entanglement for a two-qubit Ising model. One of the spin qubits is driven by a static magnetic field applied in the direction of the Ising interaction, while the other is coupled with a rotating magnetic field. We also investigate how the entanglement can be controlled by changing the external parameters. Because of the important role of maximally entangled Bell states in quantum communication, we focus on the generalized Bell states as the initial states of the system. It is found that the entanglement evolution is independent of the initial Bell states. Moreover, we can preserve the initial maximal entanglement by adjusting the angular frequency of the rotating field or controlling the exchange coupling between spin qubits. Besides, our calculation shows that the entanglement dynamics is unaffected by the static magnetic field imposed in the direction of the Ising interaction. This is an interesting result, because, as we shall show below, this driving field can be used to control and manipulate the noncyclic geometric phase without affecting the system entanglement. Besides, the nonadiabatic and noncyclic geometric phase for evolved states of the present system are calculated and described in detail. In order to identify the unusable states for quantum communication, completely deviated from the initial maximally entangled states, we also study the fidelity between the initial Bell state and the evolved state of the system. Interestingly, we find that these unusable states can be detected by geometric quantum computation.
NASA Astrophysics Data System (ADS)
Gudyma, Iu.; Maksymov, A.; Spinu, L.
2015-10-01
The spin-crossover nanoparticles of different sizes and stochastic perturbations in external field taking into account the influence of the dimensionality of the lattice was studied. The analytical tools used for the investigation of spin-crossover system are based on an Ising-like model described using of the breathing crystal field concept. The changes of transition temperatures characterizing the systems' bistable properties for 2D and 3D lattices, and their dependence on its size and fluctuations strength were obtained. The state diagrams with hysteretic and non-hysteretic behavior regions have also been determined.
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system.
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-01-01
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena. PMID:26951775
Long-range Ising and Kitaev models: phases, correlations and edge modes
NASA Astrophysics Data System (ADS)
Vodola, Davide; Lepori, Luca; Ercolessi, Elisa; Pupillo, Guido
2016-05-01
We analyze the quantum phases of the Ising chain with anti-ferromagnetic long-range interactions decaying with distance r as 1 /rα and of a related class of fermionic Hamiltonians generalising the Kitaev chain, with hopping and pairing terms long-range. We provide the phase diagram for all exponents α, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for α < 1 , while correlation functions decay with a hybrid exponential and power-law behaviour. For the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every α. For the fermionic models we show that the edge modes, massless for α > 1 , acquire a mass for α < 1 . For the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure.
Automata and the susceptibility of the square lattice Ising model modulo powers of primes
NASA Astrophysics Data System (ADS)
Guttmann, A. J.; Maillard, J.-M.
2015-11-01
We study the full susceptibility of the Ising model modulo powers of primes. We find exact functional equations for the full susceptibility modulo these primes. Revisiting some lesser-known results on discrete finite automata, we show that these results can be seen as a consequence of the fact that, modulo 2 r , one cannot distinguish the full susceptibility from some simple diagonals of rational functions which reduce to algebraic functions modulo 2 r , and, consequently, satisfy exact functional equations modulo 2 r . We sketch a possible physical interpretation of these functional equations modulo 2 r as reductions of a master functional equation corresponding to infinite order symmetries such as the isogenies of elliptic curves. One relevant example is the Landen transformation which can be seen as an exact generator of the Ising model renormalization group. We underline the importance of studying a new class of functions corresponding to ratios of diagonals of rational functions: they reduce to algebraic functions modulo powers of primes and they may have solutions with natural boundaries. Dedicated to R J Baxter, for his 75th birthday.
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system
NASA Astrophysics Data System (ADS)
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-03-01
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.
Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system
Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng
2016-01-01
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena. PMID:26951775
Nonequilibrium dynamics of arbitrary-range Ising models with decoherence: An exact analytic solution
NASA Astrophysics Data System (ADS)
Foss-Feig, Michael; Hazzard, Kaden R. A.; Bollinger, John J.; Rey, Ana Maria
2013-04-01
The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics. In a step toward understanding this interplay, we obtain an exact analytic solution for the nonequilibrium dynamics of Ising models with arbitrary couplings (and therefore in arbitrary dimension) and subject to local Markovian decoherence. Our solution shows that decoherence significantly degrades the nonclassical correlations developed during coherent Ising spin dynamics, which relax much faster than predicted by treating decoherence and interactions separately. We also show that the competition of decoherence and interactions induces a transition from oscillatory to overdamped dynamics that is absent at the single-particle or mean-field level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. In particular, we apply our results to the NIST Penning trapped-ion experiment and show that the current experiment is capable of producing entanglement amongst hundreds of quantum spins.
Ising-nematic order in the bilinear-biquadratic model for the iron pnictides
NASA Astrophysics Data System (ADS)
Bilbao Ergueta, Patricia; Nevidomskyy, Andriy H.
2015-10-01
Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations even above the magnetic transition temperature TN, we study the spin dynamics within the frustrated Heisenberg model with biquadratic spin-spin exchange interactions. Using the Dyson-Maleev (DM) representation, which proves appropriate for all temperature regimes, we find that the spin-spin dynamical structure factors are in excellent agreement with experiment, exhibiting breaking of the C4 symmetry even into the paramagnetic region TN
Macroscopic degeneracy and order in the 3D plaquette Ising model
NASA Astrophysics Data System (ADS)
Johnston, Desmond A.; Mueller, Marco; Janke, Wolfhard
2015-07-01
The purely plaquette 3D Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, “fuki-nuke” order still exists and we confirm this with multi-canonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analyzing our measurements.
Parity Symmetry and Parity Breaking in the Quantum Rabi Model with Addition of Ising Interaction
NASA Astrophysics Data System (ADS)
Wang, Qiong; He, Zhi; Yao, Chun-Mei
2015-04-01
We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46 (2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated. Supported by the National Natural Science Foundation of China under Grant Nos. 61475045 and 11347142, the Natural Science Foundation of Hunan Province, China under Grant No. 2015JJ3092
Self-organizing Ising model of artificial financial markets with small-world network topology
NASA Astrophysics Data System (ADS)
Zhao, Haijie; Zhou, Jie; Zhang, Anghui; Su, Guifeng; Zhang, Yi
2013-01-01
We study a self-organizing Ising-like model of artificial financial markets with underlying small-world (SW) network topology. The asset price dynamics results from the collective decisions of interacting agents which are located on a small-world complex network (the nodes symbolize the agents of a financial market). The model incorporates the effects of imitation, the impact of external news and private information. We also investigate the influence of different network topologies, from regular lattice to random graph, on the asset price dynamics by adjusting the probability of the rewiring procedure. We find that a specific combination of model parameters reproduce main stylized facts of real-world financial markets.
Annealed Ising model with site dilution on self-similar structures
NASA Astrophysics Data System (ADS)
Silva, V. S. T.; Andrade, R. F. S.; Salinas, S. R.
2014-11-01
We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The statistical problem is formulated in a grand canonical ensemble, in terms of the temperature T and a chemical potential μ associated with the concentration of active magnetic sites. We use a well-known transfer-matrix method, with a number of adaptations, to write recursion relations between successive generations of this hierarchical structure. We also investigate the analogous model on the diamond hierarchical lattice (DHL). From the numerical analysis of the recursion relations, we obtain various thermodynamic quantities. In the μ →∞ limit, we reproduce the results for the uniform models: in the AN, the system is magnetically ordered at all temperatures, while in the DHL there is a ferromagnetic-paramagnetic transition at a finite value of T . Magnetic ordering, however, is shown to disappear for sufficiently large negative values of the chemical potential.
Kriz, Igor; Loebl, Martin; Somberg, Petr
2013-05-15
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.
A set of exactly solvable Ising models with half-odd-integer spin
NASA Astrophysics Data System (ADS)
Rojas, Onofre; de Souza, S. M.
2009-03-01
We present a set of exactly solvable Ising models, with half-odd-integer spin- S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin- (S,1/2) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin- S lattice. By imposing the condition that the mixed half-odd-integer spin- (S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the free fermion condition of the eight vertex model. The number of solutions for a general half-odd-integer spin- S is given by S+1/2. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.
Theory and simulation of the dynamic heat capacity of the east Ising model.
Brown, Jonathan R; McCoy, John D; Borchers, Brian
2010-08-14
A recently developed methodology for the calculation of the dynamic heat capacity from simulation is applied to the east Ising model. Results show stretched exponential relaxation with the stretching exponent, beta, decreasing with decreasing temperature. For low temperatures, the logarithm of the relaxation time is approximately proportional to the inverse of the temperature squared, which is the theoretical limiting behavior predicted by theories of facilitated dynamics. In addition, an analytical approach is employed where the overall relaxation is a composite of relaxation processes of subdomains, each with their own characteristic time. Using a Markov chain method, these times are computed both numerically and in closed form. The Markov chain results are seen to match the simulations at low temperatures and high frequencies. The dynamics of the east model are tracked very well by this analytic procedure, and it is possible to associate features of the spectrum of the dynamic heat capacity with specific domain relaxation events. PMID:20707576
Missing mass approximations for the partition function of stimulus driven Ising models
Haslinger, Robert; Ba, Demba; Galuske, Ralf; Williams, Ziv; Pipa, Gordon
2013-01-01
Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNNpat) where is L the data length, N the number of neurons and Npat the number of unique patterns in the data, contrasting with the O(L2N) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding. PMID:23898262
NASA Astrophysics Data System (ADS)
Ramazanov, M. K.; Murtazaev, A. K.; Magomedov, M. A.
2016-05-01
The thermodynamic and critical properties, and phase transitions of two-dimensional Ising model on a square lattice with competing interactions are investigated by the Monte Carlo method. Estimations are made for the magnitude relations of the next-nearest-neighbor and nearest-neighbor exchange interactions r=J2/J1 in the value ranges of 0.1≤r≤1.0. The anomalies of thermodynamic observables are shown to be present in this model on the interval 0.45≤r≤0.5. The phase diagram for the dependence of the critical temperature on a value of next-nearest neighbor interaction is plotted. A phase transition for all values in the interval 0.45≤r≤0.5 is shown to be a second order. Our data show that the temperature of the heat capacity maximum at r=0.5 tends to a finite value. The static critical exponents of the heat capacity α, susceptibility γ, order parameter β, correlation length ν, and the Fisher exponent η are calculated by means of the finite-size scaling theory. It is found that the change in next-nearest neighbor interaction value in the range 0.7≤r≤1.0 leads to nonuniversal critical behavior.
Highly optimized simulations on single- and multi-GPU systems of the 3D Ising spin glass model
NASA Astrophysics Data System (ADS)
Lulli, M.; Bernaschi, M.; Parisi, G.
2015-11-01
We present a highly optimized implementation of a Monte Carlo (MC) simulator for the three-dimensional Ising spin-glass model with bimodal disorder, i.e., the 3D Edwards-Anderson model running on CUDA enabled GPUs. Multi-GPU systems exchange data by means of the Message Passing Interface (MPI). The chosen MC dynamics is the classic Metropolis one, which is purely dissipative, since the aim was the study of the critical off-equilibrium relaxation of the system. We focused on the following issues: (i) the implementation of efficient memory access patterns for nearest neighbours in a cubic stencil and for lagged-Fibonacci-like pseudo-Random Numbers Generators (PRNGs); (ii) a novel implementation of the asynchronous multispin-coding Metropolis MC step allowing to store one spin per bit and (iii) a multi-GPU version based on a combination of MPI and CUDA streams. Cubic stencils and PRNGs are two subjects of very general interest because of their widespread use in many simulation codes.
Almost Gibbsianness and Parsimonious Description of the Decimated 2d-Ising Model
NASA Astrophysics Data System (ADS)
Le Ny, Arnaud
2013-07-01
In this paper, we complete and provide details for the existing characterizations of the decimation of the Ising model on {Z}2 in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and present the construction of global specifications consistent with the extremal decimated measures. We use them to prove that these renormalized measures are almost Gibbsian at any temperature and to analyse in detail its convex set of DLR measures. We also recall the weakly Gibbsian description and complete it using a potential that admits a quenched correlation decay, i.e. a well-defined configuration-dependent length beyond which this potential decays exponentially. We use these results to incorporate these decimated measures in the new framework of parsimonious random fields that has been recently developed to investigate probability aspects related to neurosciences.
Convergence of the Equi-Energy Sampler and Its Application to the Ising Model.
Hua, Xia; Kou, S C
2011-10-01
We provide a complete proof of the convergence of a recently developed sampling algorithm called the equi-energy (EE) sampler (Kou, Zhou, and Wong, 2006) in the case that the state space is countable. We show that in a countable state space, each sampling chain in the EE sampler is strongly ergodic a.s. with the desired steady-state distribution. Furthermore, all chains satisfy the individual ergodic property. We apply the EE sampler to the Ising model to test its efficiency, comparing it with the Metropolis algorithm and the parallel tempering algorithm. We observe that the dynamic exponent of the EE sampler is significantly smaller than those of parallel tempering and the Metropolis algorithm, demonstrating the high efficiency of the EE sampler. PMID:21969801
Hysteresis in random-field Ising model on a Bethe lattice with a mixed coordination number
NASA Astrophysics Data System (ADS)
Shukla, Prabodh; Thongjaomayum, Diana
2016-06-01
We study zero-temperature hysteresis in the random-field Ising model on a Bethe lattice where a fraction c of the sites have coordination number z = 4 while the remaining fraction 1-c have z = 3. Numerical simulations as well as probabilistic methods are used to show the existence of critical hysteresis for all values of c\\gt 0. This extends earlier results for c = 0 and c = 1 to the entire range 0≤slant c≤slant 1, and provides new insight in non-equilibrium critical phenomena. Our analysis shows that a spanning avalanche can occur on a lattice even in the absence of a spanning cluster of z = 4 sites.
The hypergeometric series for the partition function of the 2D Ising model
NASA Astrophysics Data System (ADS)
Viswanathan, G. M.
2015-07-01
In 1944 Onsager published the formula for the partition function of the Ising model for the infinite square lattice. He was able to express the internal energy in terms of a special function, but he left the free energy as a definite integral. Seven decades later, the partition function and free energy have yet to be written in closed form, even with the aid of special functions. Here we evaluate the definite integral explicitly, using hypergeometric series. Let β denote the reciprocal temperature, J the coupling and f the free energy per spin. We prove that - β f = \\ln(2 \\cosh 2K) - κ2 ~ {_4F_3} \\big[~ 1,~1,~3/2,~3/2 ~~~2,~2,~2 ;16 κ2 ~\\big] ~ , where pFq is the generalized hypergeometric function, K = βJ, and 2κ = tanh 2K sech 2K.
Effective-field theory on the kinetic spin-3/2 Ising model
NASA Astrophysics Data System (ADS)
Shi, Xiaoling; Qi, Yang
2015-11-01
The effective-field theory (EFT) is used to study the dynamical response of the kinetic spin-3/2 Ising model in the presence of a sinusoidal oscillating magnetic field. The effective-field dynamic equations are given for the honeycomb lattices (Z = 3). The dynamic order parameter, the dynamic quadrupole moment are calculated. We have found that the behavior of the system strongly depends on the crystal field interaction D. The dynamic phase boundaries are obtained, and there is no dynamic tricritical point on the dynamic phase transition line. The results are also compared with previous results which obtained from the mean-field theory (MFT) and the effective-field theory (EFT) for the square lattices (Z = 4). Different dynamic phase transition lines show that the thermal fluctuations are a key factor of the dynamic phase transition.
Long-range random transverse-field Ising model in three dimensions
NASA Astrophysics Data System (ADS)
Kovács, István A.; Juhász, Róbert; Iglói, Ferenc
2016-05-01
We consider the random transverse-field Ising model in d =3 dimensions with long-range ferromagnetic interactions which decay as a power α >d with the distance. Using a variant of the strong-disorder renormalization group method we study numerically the phase-transition point from the paramagnetic side. We find that the fixed point controlling the transition is of the strong-disorder type, and based on experience with other similar systems, we expect the results to be qualitatively correct, but probably not asymptotically exact. The distribution of the (sample dependent) pseudocritical points is found to scale with 1 /lnL , L being the linear size of the sample. Similarly, the critical magnetization scales with (lnL) χ/Ld and the excitation energy behaves as L-α. Using extreme-value statistics we argue that extrapolating from the ferromagnetic side the magnetization approaches a finite limiting value and thus the transition is of mixed order.
A theory of solving TAP equations for Ising models with general invariant random matrices
NASA Astrophysics Data System (ADS)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-03-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida-Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.
Dynamical Phase Transition in the Ising Model on a Scale-Free Network
NASA Astrophysics Data System (ADS)
Krawiecki, A.
Dynamical phase transition in the Ising model on a Barabási-Albert network under the influence of periodic magnetic field is studied using Monte-Carlo simulations. For a wide range of the system sizes N and the field frequencies, approximate phase borders between dynamically ordered and disordered phases are obtained on a plane h (field amplitude) versus T/Tc (temperature normalized to the static critical temperature without external field, Tc∝lnN). On these borders, second- or first-order transitions occur, for parameter ranges separated by a tricritical point. For all frequencies of the magnetic field, position of the tricritical point is shifted toward higher values of T/Tc and lower values of h with increasing system size, i.e. the range of critical parameters corresponding to the first-order transition is broadened.
Universality Class of the Nishimori Point in the 2D +/-J Random-Bond Ising Model
NASA Astrophysics Data System (ADS)
Honecker, A.; Picco, M.; Pujol, P.
2001-07-01
We study the universality class of the Nishimori point in the 2D +/-J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value pc = 0.1094+/-0.0002 and estimate ν = 1.33+/-0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464+/-0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point.
Universality class of the Nishimori point in the 2D +/- J random-bond Ising model.
Honecker, A; Picco, M; Pujol, P
2001-07-23
We study the universality class of the Nishimori point in the 2D +/- J random-bond Ising model by means of the numerical transfer-matrix method. Using the domain-wall free energy, we locate the position of the fixed point along the Nishimori line at the critical concentration value p(c) = 0.1094 +/- 0.0002 and estimate nu = 1.33 +/- 0.03. Then, we obtain the exponents for the moments of the spin-spin correlation functions as well as the value for the central charge c = 0.464 +/- 0.004. The main qualitative result is the fact that percolation is now excluded as a candidate for describing the universality class of this fixed point. PMID:11461639
Stochastic Resonance in the Ising Model on a BARABÁSI-ALBERT Network
NASA Astrophysics Data System (ADS)
Krawiecki, A.
Stochastic resonance is investigated in the Ising model with ferromagnetic coupling on a Barabási-Albert network, subjected to weak periodic magnetic field. Spectral power amplification as a function of temperature shows strong dependence on the number of nodes, which is related to the dependence of the critical temperature for the ferromagnetic phase transition, and on the frequency of the periodic signal. Double maxima of the spectral power amplification evaluated from the time-dependent magnetization are observed for intermediate frequencies of the periodic signal, which are also dependent on the number of nodes. In the thermodynamic limit, the height of the maxima decreases to zero and stochastic resonance disappears. Results of numerical simulations are in qualitative agreement with predictions of the linear response theory in the mean-field approximation.
Non-equilibrium steady states in two-temperature Ising models with Kawasaki dynamics
NASA Astrophysics Data System (ADS)
Borchers, Nick; Pleimling, Michel; Zia, R. K. P.
2013-03-01
From complex biological systems to a simple simmering pot, thermodynamic systems held out of equilibrium are exceedingly common in nature. Despite this, a general theory to describe these types of phenomena remains elusive. In this talk, we explore a simple modification of the venerable Ising model in hopes of shedding some light on these issues. In both one and two dimensions, systems attached to two distinct heat reservoirs exhibit many of the hallmarks of phase transition. When such systems settle into a non-equilibrium steady-state they exhibit numerous interesting phenomena, including an unexpected ``freezing by heating.'' There are striking and surprising similarities between the behavior of these systems in one and two dimensions, but also intriguing differences. These phenomena will be explored and possible approaches to understanding the behavior will be suggested. Supported by the US National Science Foundation through Grants DMR-0904999, DMR-1205309, and DMR-1244666
Britton, Joseph W; Sawyer, Brian C; Keith, Adam C; Wang, C-C Joseph; Freericks, James K; Uys, Hermann; Biercuk, Michael J; Bollinger, John J
2012-04-26
The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles. Feynman predicted that a quantum simulator--a special-purpose 'analogue' processor built using quantum bits (qubits)--would be inherently suited to solving such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction, J(i,j), on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J(i,j) proportional variant d(-a)(i,j), where 0 ≤ a ≤ 3 and d(i,j) is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb-like (a = 1), monopole-dipole (a = 2) and dipole-dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism
NASA Astrophysics Data System (ADS)
Cabrera, I.; Thompson, J. D.; Coldea, R.; Prabhakaran, D.; Bewley, R. I.; Guidi, T.; Rodriguez-Rivera, J. A.; Stock, C.
2014-07-01
The quasi-one-dimensional (1D) Ising ferromagnet CoNb2O6 has recently been driven via applied transverse magnetic fields through a continuous quantum phase transition from spontaneous magnetic order to a quantum paramagnet, and dramatic changes were observed in the spin dynamics, characteristic of weakly perturbed 1D Ising quantum criticality. We report here extensive single-crystal inelastic neutron scattering measurements of the magnetic excitations throughout the three-dimensional (3D) Brillouin zone in the quantum paramagnetic phase just above the critical field to characterize the effects of the finite interchain couplings. In this phase, we observe that excitations have a sharp, resolution-limited line shape at low energies and over most of the dispersion bandwidth, as expected for spin-flip quasiparticles. We map the full bandwidth along the strongly dispersive chain direction and resolve clear modulations of the dispersions in the plane normal to the chains, characteristic of frustrated interchain couplings in an antiferromagnetic isosceles triangular lattice. The dispersions can be well parametrized using a linear spin-wave model that includes interchain couplings and further neighbor exchanges. The observed dispersion bandwidth along the chain direction is smaller than that predicted by a linear spin-wave model using exchange values determined at zero field, and this effect is attributed to quantum renormalization of the dispersion beyond the spin-wave approximation in fields slightly above the critical field, where quantum fluctuations are still significant.
NASA Astrophysics Data System (ADS)
Hayden, Lorien; Sethna, James
We systematically analyze the nonlinear invariant scaling variables at bifurcations in the renormalization-group flow, and apply our methods to the two-dimensional random-field Ising model (RFIM). At critical points, the universal scaling functions are usually written in terms of homogeneous invariant combinations of variables, like Ltν in the finite-size scaling form for the magnetization M (T | L) ~t-β M (Ltν) , where t ~Tc - T . The renormalization-group flow for the RFIM has a pitchfork bifurcation in two dimensions, where the correlation length has been argued to diverge exponentially, ξ ~ exp 1 / 2 At2 , leading to the invariant scaling combination L / ξ ~ L / exp 1 / 2 At2 . Our analysis, inspired by normal-form theory, suggests that this exponential divergence can take a richer, more general scaling form at a generic pitchfork bifurcation. We explore possible consequences for simulations. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. . DGE-1144153.
Highlighting the Structure-Function Relationship of the Brain with the Ising Model and Graph Theory
Das, T. K.; Abeyasinghe, P. M.; Crone, J. S.; Sosnowski, A.; Laureys, S.; Owen, A. M.; Soddu, A.
2014-01-01
With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions. PMID:25276772
Highlighting the structure-function relationship of the brain with the Ising model and graph theory.
Das, T K; Abeyasinghe, P M; Crone, J S; Sosnowski, A; Laureys, S; Owen, A M; Soddu, A
2014-01-01
With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions. PMID:25276772
A fully Bayesian hidden Ising model for ChIP-seq data analysis.
Mo, Qianxing
2012-01-01
Chromatin immunoprecipitation followed by next generation sequencing (ChIP-seq) is a powerful technique that is being used in a wide range of biological studies including genome-wide measurements of protein-DNA interactions, DNA methylation, and histone modifications. The vast amount of data and biases introduced by sequencing and/or genome mapping pose new challenges and call for effective methods and fast computer programs for statistical analysis. To systematically model ChIP-seq data, we build a dynamic signal profile for each chromosome and then model the profile using a fully Bayesian hidden Ising model. The proposed model naturally takes into account spatial dependency and global and local distributions of sequence tags. It can be used for one-sample and two-sample analyses. Through model diagnosis, the proposed method can detect falsely enriched regions caused by sequencing and/or mapping errors, which is usually not offered by the existing hypothesis-testing-based methods. The proposed method is illustrated using 3 transcription factor (TF) ChIP-seq data sets and 2 mixed ChIP-seq data sets and compared with 4 popular and/or well-documented methods: MACS, CisGenome, BayesPeak, and SISSRs. The results indicate that the proposed method achieves equivalent or higher sensitivity and spatial resolution in detecting TF binding sites with false discovery rate at a much lower level. PMID:21914728
Evaluation of tranche in securitization and long-range Ising model
NASA Astrophysics Data System (ADS)
Kitsukawa, K.; Mori, S.; Hisakado, M.
2006-08-01
This econophysics work studies the long-range Ising model of a finite system with N spins and the exchange interaction J/N and the external field H as a model for homogeneous credit portfolio of assets with default probability Pd and default correlation ρd. Based on the discussion on the (J,H) phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for Pd,ρd and the normalization factor Z in terms of the model parameters N and J,H. The effect of the default correlation ρd on the probabilities P(Nd,ρd) for Nd defaults and on the cumulative distribution function D(i,ρd) are discussed. The latter means the average loss rate of the“tranche” (layered structure) of the securities (e.g. CDO), which are synthesized from a pool of many assets. We show that the expected loss rate of the subordinated tranche decreases with ρd and that of the senior tranche increases linearly, which are important in their pricing and ratings.
NASA Astrophysics Data System (ADS)
Huang, Ran; Zhang, Ling; Chen, Chong; Wu, Chengjie; Yan, Linyin
2015-07-01
The ferromagnetic Ising spins are modeled on a recursive lattice constructed from random-angled rhombus units with stochastic configurations, to study the magnetic properties of the bulk Fe-based metallic glass. The integration of spins on the structural glass model well represents the magnetic moments in the glassy metal. The model is exactly solved by the recursive calculation technique. The magnetization of the amorphous Ising spins, i.e. the glassy metallic magnet is investigated by our modeling and calculation on a theoretical base. The results show that the glassy metallic magnets have a lower Curie temperature, weaker magnetization, and higher entropy compared to the regular ferromagnet in crystal form. These findings can be understood with the randomness of the amorphous system, and agree well with other experimental observations.
Ising-like model for the two-step spin-crossover
NASA Astrophysics Data System (ADS)
Bousseksou, A.; Nasser, J.; Linares, J.; Boukheddaden, K.; Varret, F.
1992-07-01
We have analyzed an Ising-like model, in the mean-field approach, involving two “antiferromagnetically” coupled sublattices. This model simulates the so-called “two-step” spin-crossover transition, for which a precise definition is given. If both sublattices are equivalent, it implies a spontaneous breaking of symmetry which may occur within a temperature range limited by two “Néel températures”. It, also predicts a simultaneous reversal of the magnetization of the sublattices (if they are unequivalent) at a “characteristic” value of temperature. These features are analyzed simultaneously with some details. The present model fits and explains well the available experimental data concerning [ Fe(2-pic)_3] Cell_2- EtOH and Fe^II[ 5NO2 sal N(1, 4, 7, 10)] . Nous avons analysé un modèle de type Ising, à deux sous-réseaux couplés “antiferromagnétiquement”, dans l'approximation du champ moyen. Ce modèle permet de bien reproduire les transitions de spin “en deux étapes”, dont nous donnons une définition précise. Lorsque les deux sous-réseaux sont équivalents, il implique une brisure spontanée de symétrie qui peut intervenir dans un domaine de température limité par deux “températures de Néel”. De plus, lorsqu'ils sont inéquivalents, il prédit le renversement simultané de l' “aimantation” des deux sous-réseaux pour une valeur “caractéristique” de la température. Nous avons analysé en détail l'ensemble de ces effets. Ce modèle nous a permis d'ajuster et de discuter les résultats expérimentaux disponibles concernant [ Fe(2-pic)_3] Cell_2- EtOH et Fe^II[ 5NO2 sal N(1, 4, 7, 10)] .
Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies
NASA Astrophysics Data System (ADS)
Laciana, Carlos E.; Rovere, Santiago L.
2011-03-01
The well-known Ising model used in statistical physics was adapted to a social dynamics context to simulate the adoption of a technological innovation. The model explicitly combines (a) an individual's perception of the advantages of an innovation and (b) social influence from members of the decision-maker's social network. The micro-level adoption dynamics are embedded into an agent-based model that allows exploration of macro-level patterns of technology diffusion throughout systems with different configurations (number and distributions of early adopters, social network topologies). In the present work we carry out many numerical simulations. We find that when the gap between the individual's perception of the options is high, the adoption speed increases if the dispersion of early adopters grows. Another test was based on changing the network topology by means of stochastic connections to a common opinion reference (hub), which resulted in an increment in the adoption speed. Finally, we performed a simulation of competition between options for both regular and small world networks.
Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs
NASA Astrophysics Data System (ADS)
Yoon, S.; Goltsev, A. V.; Dorogovtsev, S. N.; Mendes, J. F. F.
2011-10-01
We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in these networks belongs to a given set of motifs (generalization of the configuration model). These networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs. Here a hypergraph is a generalization of a graph, where a hyperedge can connect any number of vertices. These uncorrelated hypergraphs are treelike (hypertrees), which crucially simplifies the problem and allows us to apply the belief-propagation algorithm to these loopy networks with arbitrary motifs. As natural examples, we consider motifs in the form of finite loops and cliques. We apply the belief-propagation algorithm to the ferromagnetic Ising model with pairwise interactions on the resulting random networks and obtain an exact solution of this model. We find an exact critical temperature of the ferromagnetic phase transition and demonstrate that with increasing the clustering coefficient and the loop size, the critical temperature increases compared to ordinary treelike complex networks. However, weak clustering does not change the critical behavior qualitatively. Our solution also gives the birth point of the giant connected component in these loopy networks.
Information Transfer and Criticality in the Ising Model on the Human Connectome
Marinazzo, Daniele; Pellicoro, Mario; Wu, Guorong; Angelini, Leonardo; Cortés, Jesús M.; Stramaglia, Sebastiano
2014-01-01
We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows. PMID:24705627
Ising-like transitions in the O(n) loop model on the square lattice.
Fu, Zhe; Guo, Wenan; Blöte, Henk W J
2013-05-01
We explore the phase diagram of the O(n) loop model on the square lattice in the (x,n) plane, where x is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For n>2 we find Ising-like phase transitions associated with the onset of a checkerboardlike ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one-half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of n represents a softening of its particle-particle potentials. We also determine critical points in the range -2≤n≤2. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the n>2 transition may continue into the dense phase of the n≤2 loop model, or continue as a line of n≤2 O(n) multicritical points. PMID:23767498
Nonbacktracking operator for the Ising model and its applications in systems with multiple states
NASA Astrophysics Data System (ADS)
Zhang, Pan
2015-04-01
The nonbacktracking operator for a graph is the adjacency matrix defined on directed edges of the graph. The operator was recently shown to perform optimally in spectral clustering in sparse synthetic graphs and have a deep connection to belief propagation algorithm. In this paper we consider nonbacktracking operator for Ising model on a general graph with a general coupling distribution and study the spectrum of this operator analytically. We show that spectral algorithms based on this operator is equivalent to belief propagation algorithm linearized at the paramagnetic fixed point and recovers replica-symmetry results on phase boundaries obtained by replica methods. This operator can be applied directly to systems with multiple states like Hopfield model. We show that spectrum of the operator can be used to determine number of patterns that stored successfully in the network, and the associated eigenvectors can be used to retrieve all the patterns simultaneously. We also give an example on how to control the Hopfield model, i.e., making network more sparse while keeping patterns stable, using the nonbacktracking operator and matrix perturbation theory.
NASA Astrophysics Data System (ADS)
Komura, Yukihiro; Okabe, Yutaka
2014-03-01
We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Catalogue identifier: AERM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5632 No. of bytes in distributed program, including test data, etc.: 14688 Distribution format: tar.gz Programming language: C, CUDA. Computer: System with an NVIDIA CUDA enabled GPU. Operating system: System with an NVIDIA CUDA enabled GPU. Classification: 23. External routines: NVIDIA CUDA Toolkit 3.0 or newer Nature of problem: Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices. Solution method: GPU-based Swendsen-Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2]. Restrictions: The system size is limited depending on the memory of a GPU. Running time: For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc. References: [1] K
Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions.
de la Rocha, André R; de Oliveira, Paulo Murilo C; Arenzon, Jeferson J
2015-04-01
A measure of cluster size heterogeneity (H), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d=2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed. PMID:25974445
Domain-size heterogeneity in the Ising model: Geometrical and thermal transitions
NASA Astrophysics Data System (ADS)
de la Rocha, André R.; de Oliveira, Paulo Murilo C.; Arenzon, Jeferson J.
2015-04-01
A measure of cluster size heterogeneity (H ), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011), 10.1103/PhysRevE.84.020101] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d =2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed.
Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures
NASA Astrophysics Data System (ADS)
Abeling, Nils; Kehrein, Stefan
The recently discovered Dynamical Phase Transition denotes non-analytic behavior in the real time evolution of quantum systems in the thermodynamic limit and has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this talk we present the extension of the analysis to non-zero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at non-zero temperatures still displays features derived from the zero temperature non-analyticities, it is shown that in this model dynamical phase transitions do not exist if T > 0 . This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free energy density. This work was supported through CRC SFB 1073 (Project B03) of the Deutsche Forschungsgemeinschaft (DFG).
Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks
NASA Astrophysics Data System (ADS)
Krasnytska, M.; Berche, B.; Holovatch, Yu; Kenna, R.
2016-04-01
We analyse the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P(k) ˜ k -λ . We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ > 5, reproduces the zeros for the Ising model on a complete graph. For 3 < λ < 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 < λ < 5. Whereas in the former case the zeros are purely imaginary, they have a non zero real part in latter case, so that the celebrated Lee-Yang circle theorem is violated.
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering
NASA Astrophysics Data System (ADS)
Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay
2016-01-01
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
Quantum correlated cluster mean-field theory applied to the transverse Ising model
NASA Astrophysics Data System (ADS)
Zimmer, F. M.; Schmidt, M.; Maziero, Jonas
2016-06-01
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Study of spin crossover nanoparticles thermal hysteresis using FORC diagrams on an Ising-like model
NASA Astrophysics Data System (ADS)
Atitoaie, Alexandru; Tanasa, Radu; Stancu, Alexandru; Enachescu, Cristian
2014-11-01
Recent developments in the synthesis and characterization of spin crossover (SCO) nanoparticles and their prospects of switching at molecular level turned these bistable compounds into possible candidates for replacing the materials used in recording media industry for development of solid state pressure and temperature sensors or for bringing contributions in engineering. Compared to bulk samples with the same chemical structure, SCO nanoparticles display different characteristics of the hysteretic and relaxation properties like the shift of the transition temperature towards lower values along with decrease of the hysteresis width with nanoparticles size. Using an Ising-like model with specific boundary conditions within a Monte Carlo procedure, we here reproduce most of the hysteretic properties of SCO nanoparticles by considering the interaction between spin crossover edge molecules and embedding surfactant molecules and we propose a complex analysis concerning the effect of the interactions and sizes during the thermal transition in systems of SCO nanoparticles by using the First Order Reversal Curves diagram method and by comparison with similar effects in mixed crystal systems.
The dynamic critical properties of the spin-2 Ising model on a bilayer square lattice
NASA Astrophysics Data System (ADS)
Temizer, Ümüt; Yarar, Semih; Tülek, Mesimi
2016-05-01
The spin-2 Ising model is investigated for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions on the two-layer square lattice by using the Glauber-type stochastic dynamics. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip. By employing the Master equation and Glauber transition rates, the dynamic equations of the system are obtained. These equations are solved by using the numerical methods. First, we investigate the average order parameters as a function of the time to find the phases in the system. Then, the temperature-dependence of the dynamic order parameters is examined to obtain the dynamic phase transition temperatures. The dynamic phase diagrams are presented on the different planes. According to the values of the system parameters, a variety of dynamic critical points such as tricritical point, triple point, quadruple point, critical end point, double critical end point, zero-temperature critical point, multicritical point and tetracritical point are obtained. The reentrant behavior is seen in the system for the AFM/AFM interaction. Finally, we also investigate the influence of the oscillating field frequency on the dynamic phase diagrams in detail.
Minority-spin dynamics in the nonhomogeneous Ising model: Diverging time scales and exponents
NASA Astrophysics Data System (ADS)
Mullick, Pratik; Sen, Parongama
2016-05-01
We investigate the dynamical behavior of the Ising model under a zero-temperature quench with the initial fraction of up spins 0 ≤x ≤1 . In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite-size scaling is valid here. In two dimensions, however, the persistence probabilities are no longer algebraic; in particular for x ≤0.5 , persistence for the up (minority) spins shows the behavior Pmin(t ) ˜t-γexp[-(t/τ ) δ] with time t , while for the down (majority) spins, Pmaj(t ) approaches a finite value. We find that the timescale τ diverges as (xc-x ) -λ, where xc=0.5 and λ ≃2.31 . The exponent γ varies as θ2 d+c0(xc-x ) β where θ2 d≃0.215 is very close to the persistence exponent in two dimensions; β ≃1 . The results in two dimensions can be understood qualitatively by studying the exit probability, which for different system size is found to have the form E (x ) =f [(x/-xc xc) L1 /ν] , with ν ≈1.47 . This result suggests that τ ˜Lz ˜ , where z ˜=λ/ν =1.57 ±0.11 is an exponent not explored earlier.
Hysteresis in DNA compaction by Dps is described by an Ising model.
Vtyurina, Natalia N; Dulin, David; Docter, Margreet W; Meyer, Anne S; Dekker, Nynke H; Abbondanzieri, Elio A
2016-05-01
In all organisms, DNA molecules are tightly compacted into a dynamic 3D nucleoprotein complex. In bacteria, this compaction is governed by the family of nucleoid-associated proteins (NAPs). Under conditions of stress and starvation, an NAP called Dps (DNA-binding protein from starved cells) becomes highly up-regulated and can massively reorganize the bacterial chromosome. Although static structures of Dps-DNA complexes have been documented, little is known about the dynamics of their assembly. Here, we use fluorescence microscopy and magnetic-tweezers measurements to resolve the process of DNA compaction by Dps. Real-time in vitro studies demonstrated a highly cooperative process of Dps binding characterized by an abrupt collapse of the DNA extension, even under applied tension. Surprisingly, we also discovered a reproducible hysteresis in the process of compaction and decompaction of the Dps-DNA complex. This hysteresis is extremely stable over hour-long timescales despite the rapid binding and dissociation rates of Dps. A modified Ising model is successfully applied to fit these kinetic features. We find that long-lived hysteresis arises naturally as a consequence of protein cooperativity in large complexes and provides a useful mechanism for cells to adopt unique epigenetic states. PMID:27091987
NASA Astrophysics Data System (ADS)
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
2005-10-01
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighbouring singular points, of Fuchsian differential equations of quite large orders, such as those found for the third and fourth contribution (χ(3) and χ(4)) to the magnetic susceptibility of the square lattice Ising model. We deduce all the critical behaviours of the solutions χ(3) and χ(4), as well as the asymptotic behaviour of the coefficients in the corresponding series expansions. We confirm that the newly found quadratic singularities of the Fuchsian ODE associated with χ(3) are not singularities of the particular solution χ(3) itself. We use the previous connection matrices to get the exact expressions of all the monodromy matrices of the Fuchsian differential equation for χ(3) (and χ(4)) expressed in the same basis of solutions. These monodromy matrices are the generators of the differential Galois group of the Fuchsian differential equations for χ(3) (and χ(4)), whose analysis is just sketched here. As far as the physics implications of the solutions are concerned, we find challenging qualitative differences when comparing the corrections to scaling for the full susceptibility χ at high temperature (respectively low temperature) and the first two terms χ(1) and χ(3) (respectively χ(2) and χ(4)).
NASA Astrophysics Data System (ADS)
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
2006-06-01
We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions χ(3) and χ(4) of the square lattice Ising model susceptibility. An analysis of some mathematical properties of these Fuchsian differential equations is sketched. For instance, we study the factorization properties of the corresponding linear differential operators, and consider the singularities of the three and four-particle contributions χ(3) and χ(4), versus the singularities of the associated Fuchsian ordinary differential equations, which actually exhibit new ''Landau-like'' singularities. We sketch the analysis of the corresponding differential Galois groups. In particular we provide a simple, but efficient, method to calculate the so-called ''connection matrices'' (between two neighboring singularities) and deduce the singular behaviors of χ(3) and χ(4). We provide a set of comments and speculations on the Fuchsian ordinary differential equations associated with the n-particle contributions χ(n) and address the problem of the apparent discrepancy between such a holonomic approach and some scaling results deduced from a Painlevé oriented approach.
Operator product expansion coefficients of the 3D Ising model with a trapping potential
NASA Astrophysics Data System (ADS)
Costagliola, Gianluca
2016-03-01
Recently the operator product expansion coefficients of the 3D Ising model universality class have been calculated by studying via Monte Carlo simulation the two-point functions perturbed from the critical point with a relevant field. We show that this method can be applied also when the perturbation is performed with a relevant field coupled to a nonuniform potential acting as a trap. This setting is described by the trap size scaling ansatz, which can be combined with the general framework of the conformal perturbation in order to write down the correlators ⟨σ (r )σ (0 )⟩, ⟨σ (r )ɛ (0 )⟩ and ⟨ɛ (r )ɛ (0 )⟩, from which the operator product expansion coefficients can be estimated. We find Cσɛ σ=1.051 (3 ), in agreement with the results already known in the literature, and Cɛɛ ɛ=1.32 (15 ), confirming and improving the previous estimate obtained in the uniform perturbation case.
Spinodals of the Ising model on the order-4 pentagonal tiling of the hyperbolic plane
NASA Astrophysics Data System (ADS)
Richards, Howard L.
In the Euclidean plane, the Ising model on a regular lattice does not have a true spinodal - that is, there is no local minimum of the free energy that persists forever (in the limit of infinitely large systems) except for the global minimum, which characterizes the stable state. However, a local minimum can persist for a very long time, so the minimum can be referred to as a ``metastable'' state. The manner in which the metastable state decays depends on the strength of the magnetic field and the system size; the ``thermodynamic spinodal'' is the transition between systems large enough to contain a single critical droplet and systems that are too small to do so, and the ``dynamic spinodal'' marks the transition between decay as a Poisson process to decay that is ``deterministic'', meaning the standard deviation of the lifetime of the metastable state is small compared with its mean value. However, in the hyperbolic plane, true metastability exists, and evidence shows that the thermodynamic spinodal and dynamic spinodal are numerically close to the true spinodal, the field below which the metastable state cannot decay through the nucleation and growth of droplets. This research was supported by NSF Grant OCI-1005117.