We have developed an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with highly anisotropic exchange interactions. Both correlation time and real CPU time are reduced drastically. The algorithm is demonstrated in the layered triangular-lattice antiferromagnetic Ising model. We have obtained the relation between the transition temperature and the exchange interaction parameters, which modifies the result of the chain-mean-field theory.
The unusual thermodynamic properties of the Ising antiferromagnet supplemented with a ferromagnetic, mean-field term are outlined. This simple model is inspired by more realistic models of spin-crossover materials. The phase diagram is estimated using Metropolis Monte Carlo methods, and differences with preliminary Wang-Landau Monte Carlo results for small systems are noted.
We investigate as a member of the Ising universality class the Next-Nearest Neighbour Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility ratio, which should be universal quantities at the critical point, were shown to vary for small negative next-nearest neighbour interactions.
Effective Curie temperatures measured in Fe monolayer strips agree reasonable with computer sinulations of two-dimensional Ising model strips. The simulations confirm the domain structure seen already by Albano et al.
The Monte Carlo with Absorbing Markov Chains (MCAMC) method is introduced. This method is a generalization of the rejection-free method known as the $n$-fold way. The MCAMC algorithm is applied to the study of the very low-temperature properties of the lifetime of the metastable state of Ising ferromagnets. This is done both for square-lattice and cubic-lattice nearest-neighbor models. Comparison is made with exact low-temperature predictions, in particular the low-temperature predictions that the metastable lifetime is discontinuous at particular values of the field. This discontinuity for th…
Extensive Monte Carlo simulations in the semi-grand-canonical ensemble are used to study the critical behavior of a three-dimensional compressible Ising model with antiferromagnetic interactions under constant volume conditions. Elastic forces between spins are introduced by the Stillinger-Weber potential and energy parameters are chosen in such a way that antiparallel spin ordering is favored, analogous to the antiferromagnetic coupling in the rigid Ising Hamiltonian. All the quantities analyzed strongly indicate that the system remains in the universality class of the standard (rigid) three-…
We present a surprisingly simple approach to high-accuracy calculations of critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.
Ising Monte Carlo simulations of the random-field Ising system Fe(0.80)Zn(0.20)F2 are presented for H=10T. The specific heat critical behavior is consistent with alpha approximately 0 and the staggered magnetization with beta approximately 0.25 +- 0.03.
The influence of correlated impurities on the critical behaviour of the 3D Ising model is studied using Monte Carlo simulations. Spins are confined into the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behaviour of this magnetic system. Finite size scaling is used to estimate critical couplings and exponents. Long-range correlated disorder does not affect critical behavior. Asymptotic exponents differ from those of the pure 3D Ising model (3DIS), but it is impossible, with our precision, to disting…
We introduce a Generalized Loop Move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's low-energy states consist of an extensive number of degenerate or near-degenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and near-degenerate sets of configurations ar…
This discussion serves as an introduction to the use of Monte Carlo simulations as a useful way to evaluate the observables of a ferromagnet. Key background is given about the relevance and effectiveness of this stochastic approach and in particular the applicability of the Metropolis-Hastings algorithm. Importantly the potentially devastating effects of spontaneous magnetization are highlighted and a means to avert this is examined. An Ising model is introduced and used to investigate the properties of a two dimensional ferromagnet with respect to its magnetization and energy at varying tempe…
We present a simple approach to high-accuracy calculations of critical properties for the three-dimensional Ising model, without prior knowledge of the critical temperature. The iterative method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group trajectory. We found experimentally that the iterative method enables the calculation of the critical temperature simultaneously with a critical exponent.
Monte Carlo investigations of magnetization versus field, $M_c(H)$, at the critical temperature provide direct accurate results on the critical exponent $δ^{-1}$ for one, two, three and four-dimensional lattices: $δ_{1D}^{-1}$=0, $δ_{2D}^{-1}$=0.0666(2)$\simeq$1/15, $δ_{3D}^{-1}$=0.1997(4)$\simeq$1/5, $δ_{4D}^{-1}$=0.332(5)$\simeq$1/3. This type of Monte Carlo data on $δ$, which is not easily found in studies of Ising lattices in the current literature, as far as we know, defines extremely well the numerical value of this exponent within very stringent limits.
The Ising model S=1/2 and the S=1 model are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well known 2d Ising model exact values. A detailed finite…
A two-dimensional fluid of hard spheres each having a spin $\pm 1$ and interacting via short-range Ising-like interaction is studied near the second order phase transition from the paramagnetic gas to the ferromagnetic gas phase. Monte Carlo simulation technique and the multiple histogram data analysis were used. By measuring the finite-size behaviour of several different thermodynamic quantities,we were able to locate the transition and estimate values of various static critical exponents. The values of exponents $β/ν$ and $γ/ν$ are close to the ones for the two-dimensional lattice Ising mode…
In this paper, we theoretically study the critical properties of the classical spin-1 Ising model using two approaches: 1) the analytical low-temperature series expansion and 2) the numerical Metropolis Monte Carlo technique. Within this analysis, we discuss the critical behavior of one-, two- and three-dimensional systems modeled by the first-neighbor spin-1 Ising model for different types of exchange interactions. The comparison of the results obtained according the Metropolis Monte Carlo simulations allows us to highlight the limits of the widely used mean-field theory approach. We also sho…
We use Monte Carlo simulations to study multicritical properties of an Ising metamagnet in an external field. According to the mean field theory predictions, a three-dimensional layered metamagnet is expected to display a tricritical point decomposition to a critical endpoint and a bicritical endpoint, when a ratio between intralayer ferromagnetic and interlayer antiferromagnetic couplings becomes sufficiently small. Our simulations show no evidence of such a decomposition and produce a tricritical behaviour even for a coupling ratio as small as R=0.01.
This paper has a pedagogical introduction. We describe the correct method for performing Monte Carlo simulations of Ising model systems with spin greater than one half. Correct and incorrect procedures are clearly outlined and the consequences of using the incorrect procedure are shown. The difference between Kawasaki and Glauber dynamics is then outlined and both methods are applied to the antiferromagnetic square and triangular lattices for S =1.
A model based on microcanonical Monte Carlo method is used to study the application of the temperature gradient along a two-dimensional (2D) Ising system. We estimate the system size effects on thermal conductivity, $K$, for a nano-scale Ising layer with variable size. It is shown that $K$ scales with size as $ K=cL^α$ where $α$ varies with temperature. Both the Metropolis and Cruetz algorithms have been used to establish the temperature gradient. Further results show that the average demon energy in the presence of an external magnetic field is zero for low temperatures.
We derive a direct connection between Monte Carlo time and physical time in terms of physical parameters, using a quantum Hamiltonian with a $d$-dimensional phonon heat bath interacting with a square-lattice Ising ferromagnet. Based on the calculated transition rates, we perform dynamic Monte Carlo simulations using absorbing Markov chains to measure the lifetimes of the metastable state at low temperatures. We also calculate the lifetimes analytically using absorbing Markov chains. The phonon dynamic gives field-dependent prefactors in the lifetimes at low temperatures, that are different fro…
We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time t and by Monte Carlo simulation. Both the magnetization (m) and energy series are obtained up to 12-th order. An accurate estimate from series analysis for the dynamical critical exponent z is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, z_eff(t) = - {1/8} d ln t /d ln m, directly from a ratio of three-spin correlation to m. Extrapolation to t = infinity leads to an estimate z = 2.169 +/- 0.003.
We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpiński fractal with Hausdorff dimension $d_f\simeq 1.8928$. This method is shown to be relevant to the calculation of the critical temperature $T_c$ and the magnetic eigen-exponent $y_h$ on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigen-exponent $y_t$. At last, the results are shown to be consistent with a finite size scaling analysis.
The spin wave interference is studied in two dimensional Ising ferromagnet driven by two coherent spherical magnetic field waves by Monte Carlo simulation. The spin waves are found to propagate and interfere according to the classic rule of interference pattern generated by two point sources. The interference pattern of spin wave is observed in one boundary of the lattice. The interference pattern is detected and studied by spin flip statistics at high and low temperatures. The destructive interference is manifested as the large number of spin flips and vice versa.
A cluster Monte Carlo method for systems of classical spins with purely dipolar couplings is presented. It is tested and applied for finite arrays of perpendicular Ising dipoles on the triangular lattice. This model is a modification with long-range interactions of the geometrically frustrated Ising antiferromagnet. From measurements of integrated autocorrelation times for energy, magnetization and staggered magnetizations, a high efficiency of the cluster Monte Carlo (MC) algorithm compared to a single-spin-flip algorithm is found. For the investigated model, a finite temperature transition i…
The Monte Carlo analysis for the magnetic response of a single-walled nanotube using the Metropolis and Wang Landau algorithms is reported in the present paper. The nanotube architecture used in the present study utilizes the spin half Ising model with nearest neighbors interaction and obtained various magnetic orderings namely, ferromagnetic, G-type anti-ferromagnetic, A-type anti-ferromagnetic, and C-type anti-ferromagnetic. It is also found that the phase changes from ferromagnetic/anti-ferromagnetic to paramagnetic with the modification of system's control parameters. The transition temper…
The Ising model shows on growing Barabasi - Albert networks the same ferromagnetic behavior as on static Barabasi - Albert networks. Sznajd models on growing Barabasi - Albert networks show an hysteresis like behavior. Nearly a full consensus builds up and the winning opinion depends on history. On slow growing Barabasi - Albert networks a full consensus builds up. At five opinions in the Sznajd model with limited persuasion on growing Barabasi - Albert networks, all odd opinions win and all even opinions loose supporters.
Monte Carlo simulations of the magnetization temperature dependence in $D\times L$ nanotubes (periodic lateral boundary conditions) and nanostrips (free lateral boundary conditions) with $D$=8, 16, 32, 64$\ll L\longrightarrow 5000$ have been performed. The apparent critical temperature was determinated using the Binder Cumulant method (crossing of data for $D\times L$ with data for $D\times 2L)$ and it was found to be $ T_{C}=0 $ for small $D$ values $(D<D^{\ast})$, as it might have been expected.
With the help of the replica exchange Monte Carlo method and the improved Monte Carlo renormalization-group scheme, we investigate over a wide area in the phase diagram of the Gaussian random field Ising model on the simple cubic lattice. We found that the phase transition at a weak random field belongs to the same universality class as the zero-temperature phase transition. We also present a possible scenario for the replica symmetry breaking transition.
We present an extensive Monte Carlo investigation of the metastable lifetime through the reversal of the magnetization of spin-$s$ Ising and Blume-Capel models, where $s=\{1/2, 1, 3/2, 2, 5/2, 3, 7/2\}$. The mean metastable lifetime (or reversal time) is studied as a function of the applied magnetic field and for both models is found to obey the Becker-Doring theory, as was initially developed for the case of $s=1/2$ Ising ferromagnet within the classical nucleation theory. Moreover, the decay of metastable volume fraction nicely follows the Avrami's law for all values of $s$ and for both mode…
The dynamical critical exponent $z$ is a fundamental quantity in characterizing quantum criticality, and it is well known that the presence of dissipation in a quantum model has significant impact on the value of $z$. Studying quantum Ising spin models using Monte Carlo methods, we estimate the dynamical critical exponent $z$ and the correlation length exponent $ν$ for different forms of dissipation. For a two-dimensional quantum Ising model with Ohmic site dissipation, we find $z \approx 2$ as for the corresponding one-dimensional case, whereas for a one-dimensional quantum Ising model with O…
An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors time clocks current in a global sense. Boundary conflicts are rigorously solved by adopting a chessboard decomposition into non-interacting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of the serial…
We have investigated by Monte-Carlo simulation the phase diagram of a three-dimensional Ising model with nearest-neighbor ferromagnetic interactions and small, but long-range (Coulombic) antiferromagnetic interactions. We have developed an efficient cluster algorithm and used different lattice sizes and geometries, which allows us to obtain the main characteristics of the temperature-frustration phase diagram. Our finite-size scaling analysis confirms that the melting of the lamellar phases into the paramgnetic phase is driven first-order by the fluctuations. Transitions between ordered phases…
The dynamical responses of Ising metamagnet (layered antiferromagnet) in the presence of a sinusoidally oscillating magnetic field are studied by Monte Carlo simulation. The time average staggered magnetisation plays the role of dynamic order parameter. A dynamical phase transition was observed and a phase diagram was plotted in the plane formed by field amplitude and temperature. The dynamical phase boundary is observed to shrink inward as the relative antiferromagnetic strength decreases. The results are compared with that obtained from pure ferromagnetic system. The shape of dynamic phase b…
With the developed "extended Monte Calro" (EMC) algorithm, we have studied the depinning transition in Ising-type lattice models by extensive numerical simulations, taking the random-field Ising model with a driving field and the driven bond-diluted Ising model as examples. In comparison with the usual Monte Carlo method, the EMC algorithm exhibits greater efficiency of the simulations. Based on the short-time dynamic scaling form, both the transition field and critical exponents of the depinning transition are determined accurately via the large-scale simulations with the lattice size up to L…
The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most approaches do not generalise to arbitrary lattices and couplings. We present a formalism that allows one to apply Hybrid Monte Carlo (HMC) simulations to the Ising model, demonstrating how a system with discrete degrees of freedom can be simulated with continuous variables. Because of the flexibility of HMC, our formalism is easily generalizable to arbitrary …
A kinetic Ising model is analyzed where spin variables correspond to lattice cells with mobile or immobile particles. Introducing additional restrictions for the flip processes according to the n-spin facilitated kinetic Ising model and using Monte Carlo methods we study the freezing process under the influence of an additional nearest-neighbor interaction. The stretched exponential decay of the auto-correlation function is observed and the exponent $γ$ as well as the relaxation time are determined depending on the activation energy $h$ and the short range coupling $J$. The magnetization corre…
While the 3d Ising model has defied analytic solution, various numerical methods like Monte Carlo, MCRG and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quanti…
We study the thermodynamic and magnetic properties of an Ising bilayer ferrimagnet. The system is composed of two interacting non-equivalent planes in which the intralayer couplings are ferromagnetic while the interlayer interactions are antiferromagnetic. Moreover, one of the planes is randomly diluted. The study is carried out within a Monte Carlo approach employing the multiple histogram reweighting method and finite-size scaling tools. The occurrence of a compensation phenomenon is verified and the compensation temperature, as well as the critical temperature for the model, are obtained as…
We present an extensive analysis of systematic deviations in Wolff cluster simulations of the critical Ising model, using random numbers generated by binary shift registers. We investigate how these deviations depend on the lattice size, the shift-register length, and the number of bits correlated by the production rule. They appear to satisfy scaling relations.
A Metropolis Monte Carlo simulation is used in this paper to investigate the temperature dependency of the hysteresis loops of a spin-1 bilayer with square monolayers. In this system, the atoms interact ferromagnetically in-plane, with either ferromagnetic or antiferromagnetic interplane interactions. The effects of four distinct combinations of the Hamiltonian parameters on the hysteresis behaviours are discussed in detail. The geometry of the hysteresis loops changes depending on how the exchange couplings are combined. With ferromagnetic interlayer coupling, only the central hysteresis loop…
Magnetic properties of an Ising bilayer system defined on a honeycomb lattice with non-magnetic interlayers which interact via an indirect exchange coupling have been investigated by Monte Carlo simulation technique. Equilibrium properties of the system exhibit ferrimagnetism with $P$-, $N$- and $Q$- type behaviors. Compensation phenomenon suddenly disappears with decreasing strength of indirect ferrimagnetic interlayer exchange coupling. Qualitative properties are in a good agreement with those obtained by effective field theory. In order to investigate the stochastic dynamics of kinetic Isin…
Binary magnetic square lattice Ising system with nearest neighbour interactions were simulated using the Monte Carlo technique. Two types of ions were randomly distributed on the lattice sites, one type interacting ferromagnetic and the other antiferromagnetic. A phase diagram of the ion concentration dependent critical temperature, Tc was deduced. Combined Bethe Peierls approximation and Mean Field theory phase transition results were compared to the results of the present method. An improved accuracy of the approximations of the critical temperatures was observed. The Monte Carlo simulation …
The non-equilibrium dynamics of the three-dimensional Edwards-Anderson spin-glass model with different bond distributions is investigated by means of Monte Carlo simulation. A numerical method is used to determine the critical temperature and the scaling exponents of the correlation and the integrated response functions. The results obtained agree with those calculated in equilibrium simulations and suggest that the universality class does not depend on the exact form of the bond distribution.
In this work we study the two and three-dimensional antiferromagnetic Ising model with an imaginary magnetic field $iθ$ at $θ=π$. In order to perform numerical simulations of the system we introduce a new geometric algorithm not affected by the sign problem. Our results for the $2D$ model are in agreement with the analytical solutions. We also present new results for the $3D$ model which are qualitatively in agreement with mean-field predictions.
A careful Monte Carlo investigation of the phase transition very close to the critical point (T -> Tc, H -> 0) in relatively large d = 3, s = 1/2 Ising lattices did produce critical exponents beta = 0.3126(4) =~ 5/16, delta^{-1} = 0.1997(4) =~ 1/5 and gamma_{3D} = 1.253(4) =~ 5/4. Our results indicate that, within experimental error, they are given by simple fractions corresponding to the linear interpolations between the respective two-dimensional (Onsager) and four-dimensional (mean field) critical exponents. An analysis of our inverse susceptibility data chi^{-1}(T) vs. /T - Tc/ shows that …
In a ferromagnetic Ising system, domain pattern formation, i.e., phase-ordering, occurs after a sudden quench. We propose the method to simulate the pattern formation dynamics by an Ising machine. We demonstrate that the method reproduces domain patterns similar to those simulated by the Monte Carlo method. Moreover, the same domain growth law is observed in the proposed method and the Monte Carlo method.
Motivated by the recent progress in the effective string description of the interquark potential in lattice gauge theory, we study interfaces with periodic boundary conditions in the three-dimensional Ising model. Our Monte Carlo results for the associated free energy are compared with the next-to-leading order (NLO) approximation of the Nambu-Goto string model. We find clear evidence for the validity of the effective string model at the level of the NLO truncation.
We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain $z=2.0245(15)$ for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our …
Critical and in the highly frustrated regime also dynamical properties of the $J_1-J_2$ Ising model with competing nearest-neighbor $J_1$ and second-nearest-neighbor $J_2$ interactions on a honeycomb lattice are investigated by standard Monte Carlo and parallel tempering simulations. The phase boundary is determined as a function of the coupling ratio for the phase transition between the paramagnetic and ferromagnetic states within $R \equiv J_2/|J_1| \in [-1/4,0]$. It is confirmed that at least for $R \geq -0.2$ the transition remains second-order and complies with the standard Ising universa…
We apply numerical simulations to study the criticality of the 3D Ising model with random site quenched dilution. The emphasis is given to the issues not being discussed in detail before. In particular, we attempt a comparison of different Monte Carlo techniques, discussing regions of their applicability and advantages/disadvantages depending on the aim of a particular simulation set. Moreover, besides evaluation of the critical indices we estimate the universal ratio $Γ^+/Γ^-$ for the magnetic susceptibility critical amplitudes. Our estimate $Γ^+/Γ^- = 1.67 \pm 0.15$ is in a good agreement wi…
We study the critical properties of a two--dimensional Ising model with competing ferromagnetic exchange and dipolar interactions, which models an ultra-thin magnetic film with high out--of--plane anisotropy in the monolayer limit. We present numerical evidence showing that two different scenarios appear in the model for different values of the exchange to dipolar intensities ratio, namely, a single first order stripe - tetragonal phase transition or two phase transitions at different temperatures with an intermediate Ising nematic phase between the stripe and the tetragonal ones. Our results …
In this work we study a disordered binary Ising model on the square lattice. The model system consists of two different particles with spin-1/2 and spin-1, which are randomly distributed on the lattice. It has been considered only spin nearest-neighbor exchange interactions with $J>0$. This system can represent a disordered magnetic binary alloy $A_{x}B_{1-x}$, obtained from the high temperature quenching of a liquid mixture. The results were obtained by the use of Monte Carlo simulations for several lattice sizes $L$, temperature $T$ and concentration $x$ of ions $A$ with spin-1/2. We found i…
We present a Monte Carlo study of the magnetic properties of an Ising multilayer ferrimagnet. The system consists of two kinds of non-equivalent planes, one of which is site-diluted. All intralayer couplings are ferromagnetic. The different kinds of planes are stacked alternately and the interlayer couplings are antiferromagnetic. We perform the simulations using the Wolff algorithm and employ multiple histogram reweighting and finite-size scaling methods to analyze the data with special emphasis on the study of compensation phenomena. Compensation and critical temperatures of the system are o…
We study the three-dimensional Ising model at the critical point in the fixed-magnetization ensemble, by means of the recently developed geometric cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in terms of microscopic spin-up and spin-down probabilities in a given configuration of neighbors. In the thermodynamic limit, the relation between this field and the magnetization reduces to the canonical relation M(h). However, for finite systems, the relation is different. We establish a close connection between this relation and the probability distribution of the magnetizat…
We investigate the behavior of the deviation of the estimator for the density of states (DOS) with respect to the exact solution in the course of Wang-Landau and Stochastic Approximation Monte Carlo (SAMC) simulations of the two-dimensional Ising model. We find that the deviation saturates in the Wang-Landau case. This can be cured by adjusting the refinement scheme. To this end, the 1/t-modification of the Wang-Landau algorithm has been suggested. A similar choice of refinement scheme is employed in the SAMC algorithm. The convergence behavior of all three algorithms is examined. It turns out…
An Ising model for damage spreading with a probability of damage healing ($q = 1 - p$) is proposed and studied by means of Monte Carlo simulations. In the limit $p \to 1$ the new model is mapped to the standard Ising model. It is found that, for temperatures above the Onsager critical temperature ($T_{C}$), there exist a no trivial finite value of $p$ that sets the critical point ($p_{c}$) for the onset of damage spreading. It is found that $p_{c}$ depends on $T$, defining a critical curve at the border between damage spreading and damage healing. Transitions along such curve are found to belo…
The equilibrium phase behavior of microphase-forming systems is notoriously difficult to obtain because of the extended metastability of their modulated phases. In this paper we present a systematic simulation methodology for studying layered microphases and apply the approach to two prototypical lattice-based systems: the three-dimensional axial next-nearest-neighbor Ising (ANNNI) and Ising-Coulomb (IC) models. The method involves thermodynamically integrating along a reversible path established between a reference system of free spins under an ordering field and the system of interest. The r…
We study the spin-spin correlation function in or near the T=0 ground state of the antiferromagnetic Ising model on a triangular lattice. At zero temperature its modulation on the sublattices gives rise to two Bragg peaks in the structure factor, and a known expression for the algebraic decay of correlations enables us to examine the form of the diffusive scattering. We do so by means of a comparison between exact results and data calculated using standard Monte Carlo techniques. At non-zero temperatures the finite correlation length alters this form, and we account for the change by proposing…
Detailed mean field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. Approximate analytical treatment of the mean field equations of motion shows the existence of diverging length and time scales across this dynamic transition phase boundary. These are also supported by numerical solutions of the complete mean field equations of motion and the Monte Carlo study of the system evolving under Glauber dynamics in both two and three dimensions. Class…
The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the two-dimensional square lattice. We extract the critical exponents $ν$ and $β$ as a function of the decay exponent of the long-range interactions. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range Gaussian universality classes, as well as the intermediate regime…
