In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures $T_1<T_c<T_2$, where $T_c$ is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase ($T<T_c$) and a disordered one ($T>T_c$) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization $m\equiv 0$ corresponding to $T=\infty$, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization $m=m_0$, we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T=0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements ($t\rightarrow\infty$) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions.
A dilute Ising ferromagnet is considered in this study using renormalization group techniques with a hierarchical lattice. A series of phase diagrams have been produced that probe the effects of varying the temperature and concentration of nonmagnetic impurities. Each phase diagram corresponds to a different strength for the internal coupling coefficients on our lattice. Phases have been interpreted and critical exponents calculated for the higher order transitions.
This paper considers a dilute Ising ferromangnet with annealed vacancies and attractive biquadratic interactions. Phase diagrams have been calculated while varying the temperature and concentration of annealed vacancies in the system while maintaining constant, attractive biquadratic couplings. These results have been produced using renormalization group analysis with a hierarchical lattice. Critical exponents have been calculated and each basin of attraction interpreted.
Calculation of thermodynamic functions of the three-dimensional Ising ferromagnet above and below critical temperature is performed in the approximation of sixfold basis distribution ($ρ^6$ model). Comparison with the results for the $ρ^4$ model indicates that dependence of the thermodynamic functions on the renormalization group parameter $s$ becomes weaker. The optimal interval of the renormalization group parameter values is determined.
We study a 3-dimensional Ising model in which the tendency to order due to short-range ferromagnetic interactions is frustrated by competing long-range (Coulombic) interactions. Complete ferromagnetic ordering is impossible for any nonzero value of the frustration parameter, but the system displays a variety of phases characterized by periodically modulated structures. We have performed extensive Monte-Carlo simulations which provide strong evidence that the microphase separation transition between paramagnetic and modulated phases is a fluctuation-induced first-order transition. Additional tr…
We study the excitation energy spectrum in the S=1/2 ferromagnetic Ising spin chain with the easy axis z in a magnetic field h={h_x,0,h_z}. According to Wu and McCoy's scenario of weak confinement, the fermionic spinon excitations (kinks), being free at h_z = 0 in the ordered phase, are coupled into bosonic bound states at arbitrary small h_z. We calculate the energy spectrum of such excitations in the leading order in small h_z, using different perturbative methods developed for the similar problem in the Ising field theory.
In the high dimension (mean field) limit the susceptibility and the second moment correlation length of the Ising ferromagnet depend on temperature as chi(T)=tau^{-1} and xi(T)=T^{-1/2}tau^{-1/2} exactly over the entire temperature range above the critical temperature T_c, with the scaling variable tau=(T-T_c)/T. For finite dimension ferromagnets temperature dependent effective exponents can be defined over all T using the same expressions. For the canonical two dimensional square lattice Ising ferromagnet it is shown that compact "extended scaling" expressions analogous to the high dimensiona…
For the inverse square long-range ferromagnetic Ising chain in a transverse field, the thermal phase boundary of the floating Kosterlitz-Thouless phase is obtained for several values of the transverse field down to the quantum critical point. The sharp domain walls in the classical model are increasingly smeared out by the transverse field, which is evidenced by a pronounced broadening of the non-universal bump in the specific heat. The discernability of KT critical scaling in finite-size simulations is discussed.
The densities of Yang-Lee zeros for the Ising ferromagnet on the $L\times L$ square lattice are evaluated from the exact grand partition functions ($L=3\sim16$). The properties of the density of Yang-Lee zeros are discussed as a function of temperature $T$ and system size $L$. The three different classes of phase transitions for the Ising ferromagnet, first-order phase transition, second-order phase transition, and Yang-Lee edge singularity, are clearly distinguished by estimating the magnetic scaling exponent $y_h$ from the densities of zeros for finite-size systems. The divergence of the den…
Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width $N$ sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the ``analytical'' correction terms, $N^{-2}$, are identically zero for triangular-- and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entir…
The fate of the Ising ferromagnet and antiferromagnet by the zero-temperature Glauber dynamics from random initial spin configuration is investigated in the two-dimensional Archimedean and 2-uniform lattices. Blinker states are found in addition to the ground state and metastable state. We show that an even-coordinated lattice can arrive at a blinker state or a metastable state without stripe structure, in contrast to common expectation. The universal relationship between the critical percolation and the probability of stripe final state is confirmed for six lattices. Results about the fate of…
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.
We report the results of the magnetisation reversal in Ising ferromagnet having thermal and field gradients by Monte Carlo simulation. We have studied the distribution of reversal times for different values of thermal and field gradients and compared the results with those obtained for uniform temperature. The movement of the domain wall of distinct domains and the growth of roughness of domain wall have also been studied statistically. The role of competing thermal and field gradients, in the reversal mechanism, was also studied and a line of marginal competition was obtained.
The mixed spin-1/2 and spin-1 Ising-Heisenberg ferromagnet on the decorated triangular lattice consisting of inter-connected diamonds is investigated within the framework of an exact decoration-iteration mapping transformation. It is shown that the diamond-like decoration by a couple of the Heisenberg spins gives rise to a diverse critical behaviour including reentrant phase transitions with two consecutive critical points.
Sznajd-Weron in [Phys. Rev. E {\bf 82}, 031120 (2010)] suggested that the one-dimensional Ising model subject to the zero temperature synchronous Glauber dynamics exhibits a discontinuous phase transition. We show here instead that the phase transition is of a continuous nature and identify critical exponents: $β\approx 0$, $ν\approx 1$, and $z \approx 2$, via a systematic finite-size scaling analysis.
We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions D <4, we derive an explicit expression for the probability distribution function (PDF) of the critical free energy fluctuations. In particular, using known fixed-point values for the renormalized coupling parameters, we obtain the universal curve for such PDF in the dimension D=3. It is demonstrated that this function is strongly asymmetric: its left tail is much slower than the right one.
We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 1/4 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales, with the longer stemming from the influence of a long-lived diagonal stripe ``defect''. In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever with…
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…
It is known that, after a quench to zero temperature ($T=0$), two-dimensional ($d=2$) Ising ferromagnets with short-range interactions do not always relax to the ordered state. They can also fall in infinitely long-lived striped metastable states with a finite probability. In this paper, we study how the abundance of striped states is affected by long-range interactions. We investigate the relaxation of $d=2$ Ising ferromagnets with power-law interactions by means of Monte Carlo simulations at both $T=0$ and $T \ne 0$. For $T=0$ and the finite system size, the striped metastable states are sup…
The zero-temperature Glauber dynamic is used to investigate the persistence probability $P(t)$ in the randomic two-dimensional ferromagnetic Ising model on a Voronoi-Delaunay tessellation. We consider the coupling factor $J$ varying with the distance $r$ between the first neighbors to be $J(r) \propto e^{-αr}$, with $α\ge 0$. The persistence probability of spins flip, that does not depends on time $t$, is found to decay to a non-zero value $P(\infty)$ depending on the parameter $α$. Nevertheless, the quantity $p(t)=P(t)-P(\infty)$ decays exponentially to zero over long times. Furthermore, the …
We present very accurate numerical estimates of the time and size dependence of the zero-temperature local persistence in the $2d$ ferromagnetic Ising model. We show that the effective exponent decays algebraically to an asymptotic value $θ$ that depends upon the initial condition. More precisely, we find that $θ$ takes one universal value $0.199(2)$ for initial conditions with short-range spatial correlations as in a paramagnetic state, and the value $0.033(1)$ for initial conditions with the long-range spatial correlations of the critical Ising state. We checked universality by working with …
In order to provide an experimental access to the statistical theory of Lee and Yang (1952) the density function g(theta) of zeros on the Lee-Yang circle has been determined for the first time by analyzing isothermal magnetization data, m(H), of the Ising ferromagnet FeCl2 in axial magnetic fields, H, at temperatures 34 < T < 99K. The validity of our approach is demonstrated by the perfect agreement of magnetic specific heat data as calculated from g(theta) and m(H) via Maxwells relation, respectively. Moreover, the correct in-plane exchange constant of FeCl2 emerges from the series expansion …
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…
We introduce a new variational approach to the stationary state of kinetic Ising-like models. The approach is based on the cluster expansion of the entropy term appearing in a functional which is minimized by the system history. We rederive a known mean-field theory and propose a new method, here called diamond approximation, which turns out to be more accurate and faster than other methods of comparable computational complexity.
Dynamic behavior of a site diluted Ising ferromagnet in the presence of periodically oscillating magnetic field has been analyzed by means of the effective field theory (EFT). Dynamic equation of motion have been solved for a honeycomb lattice ($z=3$) with the help of a Glauber type stochastic process. The global phase diagrams and the variation of the corresponding dynamic order parameter as a function of the Hamiltonian parameters and temperature has been investigated in detail and it has been shown that the system exhibits reentrant phenomena, as well as a dynamic tricritical point which di…
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…
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 diagr…
The finite size analysis of the nonequilibrium phase transition, in two dimensional Ising ferromagnet driven by plane propagating magneticwave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamicphase transition from a high temperature dynamically symmetric ({\it propagating}) phase to a low temperature dynamically symmetry-broken ({\it pinned}) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth order Binder Cumulant of the dynamic order parameter as a fun…
We show that the equilibrium interfaces in the disordered phase have critical percolation fractal dimension over a wide range of length scales. We confirm that the system falls out of equilibrium at a temperature that depends on the cooling rate as predicted by the Kibble-Zurek argument and we prove that the dynamic growing length once the cooling reaches the critical point satisfies the same scaling. We determine the dynamic scaling properties of the interface winding angle variance and we show that the crossover between critical Ising and critical percolation properties is determined by the …
By Monte Carlo simulations we study critical properties of the mixed spin-1/2 and spin-1 Ising model on a triangular lattice, considering two different ways of the spin-value distributions on the three sublattices: $(1/2,1/2,1)$ and $(1/2,1,1)$. In the former case, we find standard Ising universality class phase transitions between paramagnetic and magnetic phases but no phase transitions between two distinct magnetic phases $(\pm 1/2,\pm 1/2,\pm 1)$ and $(\pm 1/2,\pm 1/2,0)$ at any finite temperature, except for some interesting non-critical anomalies displayed by response functions. On the o…
We study an infinite range ferromagnetic Ising model in the presence of a transverse magnetic field which exhibits a quantum paramagnetic-ferromagnetic phase transition at a critical value of the transverse field. In the thermodynamic limit, the low-temperature properties of this model are dominated by the behavior of a single large classical spin governed by an anisotropic Hamiltonian. Using this property, we study the quench and AC dynamics of the model both numerically and analytically, and develop a correspondence between the classical phase space dynamics of a single spin and the quantum …
The nucleation in Ising ferromagnet has been studied by Monte Carlo simulation. Here, the magnetic field is spreading over the space in time. The nucleation time is observed to increase as compared to that in the case of static field. The clusters of negative spins is observed to grow from the center. The growth of effective magnetisation is studied with temperature and the strength of spreading magnetic field. The ratio of nucleation time and effective time is also studied with strength of spreading magnetic field. The effective time would introduce itself as a new scale of time in the case o…
We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase. We evolve the system with kinetic Monte Carlo rules that do not conserve the order parameter. We confirm the rapid approach to random critical percolation in a time-scale that diverges with the system size but is much shorter than the equilibration time. We study the scaling properties of the evolution towards critical percolation and we identify an associated growing length, different from the curvature driven one. By working with the model …
We present evidence for a deep connection between the zero-temperature coarsening of the two-dimensional kinetic Ising model (KIM) and critical continuum percolation. In addition to reaching the ground state, the KIM can also fall into a variety of topologically distinct metastable stripe states. The probability to reach a stripe state that winds a times horizontally and b times vertically on a square lattice with periodic boundary conditions equals the corresponding exactly-solved critical percolation crossing probability P_{a,b} for a spanning path with winding numbers a and b.
We study the field--temperature phase diagram of the two-dimensional dipolar Ising ferromagnet on a kagome lattice with a specific ratio between the exchange and dipolar constants, $δ= 1$. Using the stochastic cutoff (SCO) $O(N)$ Monte Carlo method, we calculated order parameters for stripe and bubble phases and other thermodynamical quantities. We find two kinds of stripe phases at low fields, where the arrangement of the branch spins neighboring the stripe frame varies, and two bubble phases at high fields, in which three-spin domains (bubbles) form a regular triangular lattice but the trian…
We investigate the temporal evolution of a ferromagnetic system of Ising spins evolving under Kawasaki dynamics from a random initial condition, in spatial dimensions one and two. We examine in detail the asymptotic behaviour of the two-time correlation and response functions. The linear response is measured without applying a field, using a recently proposed algorithm. For the chain at vanishingly small temperature, we introduce an accelerated dynamics which has the virtue of projecting the system into the asymptotic scaling regime. This allows us to revisit critically previous works on the b…
We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to $d$-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches $|H|/J=2$ at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approaches zero under these conditions. Near $|H|/J=2$ and zero temperature, th…
We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate data for large lattices with $L=8,10,12,15,20,25,30,40,50$. The spin updating algorithm we employ has the advantages of both metropolis and single-update methods. Our study indicates that the transition to be continuous at $T_c=3.6403(2)$. A convincing finite-size scaling analysis of the model yield $ν=0.9995(21)$, $β/ν=0.12400(18)$, $γ/ν=1.75223(22)$, $γ'/ν=1…
We present exact expressions for hysteresis loops in the ferromagnetic random field Ising model in the limit of zero temperature and zero driving frequency for an arbitrary initial state of the model on a Bethe lattice. This work extends earlier results that were restricted to an initial state with all spins pointing parallel to each other.
We introduce a thermal dynamics for the Ising ferromagnet where the energy variations occurring within the system exhibit a diffusive character typical of thermalizing agents such as e.g. localized excitations. Time evolution is provided by a walker hopping across the sites of the underlying lattice according to local probabilities depending on the usual Boltzmann weight at a given temperature. Despite the canonical hopping probabilities the walker drives the system to a stationary state which is not reducible to the canonical equilibrium state in a trivial way. The system still exhibits a mag…
We consider the asymptotic state after a sudden quench of the magnetic field in the transverse field quantum Ising chain starting from excited states of the pre-quench Hamiltonian. We compute the thermodynamic entropies of the generalised Gibbs and the diagonal ensembles and we find that the generalised Gibbs entropy is always twice the diagonal one. We show that particular care should be taken in extracting the thermodynamic limit since different averages of equivalent microstates give different results for the entropies.
We study the predictability of zero-temperature Glauber dynamics in various models of disordered ferromagnets. This is analyzed using two independent dynamical realizations with the same random initialization (called twins). We derive, theoretically and numerically, trajectories for the evolution of the normalized magnetization and twin overlap as the system size tends to infinity. The systems we treat include mean-field ferromagnets with light-tailed and heavy-tailed coupling distributions, as well as highly-disordered models with a variety of other geometries. In the mean-field setting with …
In the simple [hyper]cubic five dimension near neighbor interaction Ising ferromagnet, extensive simulation measurements are made of the link overlap and the spin overlap distributions. These "two replica" measurements are standard in the Spin Glass context but are not usually recorded in ferromagnet simulations. The moments and moment ratios of these distributions (the variance, the kurtosis and the skewness) show clear critical behaviors at the known ordering temperature of the ferromagnet. Analogous overlap effects can be expected quite generally in Ising ferromagnets in any dimension. The …
In this study, the temperature variations of the equilibrium and the non-equilibrium antiferromagnetic and ferromagnetic susceptibilities of a metamagnetic system are examined near the critical point. The kinetic equations describing the time dependencies of the total and staggered magnetizations are derived by utilizing linear response theory. In order to obtain dynamic magnetic relaxation behavior of the system, the stationary solutions of the kinetic equations in existence of sinusoidal staggered and physical external magnetic fields are performed. In addition, the static and dynamical mean…
In the paper the Curie temperatures of selectively diluted planar Ising ferromagnet on the triangular lattice are calculated vs. concentration of magnetic atoms. Various analytical approaches are compared with the exact numerical calculations for finite clusters, as well as with the exact analytical solutions for the triangular and honeycomb lattices.
We study the free energy distribution function of weakly disordered Ising ferromagnet in terms of the D-dimensional random temperature Ginzburg-Landau Hamiltonian. It is shown that besides the usual Gaussian "body" this distribution function exhibits non-Gaussian tails both in the paramagnetic and in the ferromagnetic phases. Explicit asymptotic expressions for these tails are derived. It is demonstrated that the tails are strongly asymmetric: the left tail (for large negative values of the free energy) is much more slow than the right one (for large positive values of the free energy). It is …
We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation functions for finite-range Ising ferromagnets in any dimensions and at any temperature above critical.
In the past decade low-temperature Glauber dynamics for the one-dimensional Ising system has been several times observed experimentally and occurred to be one of the most important theoretical approaches in a field of molecular nanomagnets. On the other hand, it has been shown recently that Glauber dynamics with the Metropolis flipping probability for the zero-temperature Ising ferromagnet under synchronous updating can lead surprisingly to the antiferromagnetic steady state. In this paper the generalized class of Glauber dynamics at zero-temperature will be considered and the relaxation into …
We investigate the ferromagnetic-glassy transitions which separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider the cubic-lattice +-J (Edwards-Anderson) Ising model with bond distribution $P(J) = p δ(J - 1) + (1-p) δ(J + 1)$, and present a numerical Monte Carlo study of the critical behavior along the line that marks the onset of ferromagnetism. The finite-size scaling analysis of the Monte Carlo data shows that the ferromagnetic-glassy transition line is slightly re…
By means of extensive computer simulations we analyze in detail the two dimensional $\pm J$ Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to ``spin glass'' like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the ``spin glass'' behavior to a paramagnetic phase for the largest volume studied.
We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the non-equilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulati…
A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Grif…
A ferromagnetic Ising chain which is endowed with a single-spin-flip Glauber dynamics is investigated. For an arbitrary annealing protocol, we derive an exact integral equation for the domain wall density. This integral equation admits an asymptotic solution in the limit of extremely slow cooling. For instance, we extract an asymptotic of the density of domain walls at the end of the cooling procedure when the temperature vanishes. Slow annealing is usually studied using a Kibble-Zurek argument; in our setting, this argument leads to approximate predictions which are in good agreement with exa…
The explicit form of the Griffiths singularity in the random ferromagnetic Ising model in external magnetic field is derived. In terms of the continuous random temperature Ginzburg-Landau Hamiltonian it is shown that in the paramagnetic phase away from the critical point the free energy as the function of the external magnetic field h in the limit h -> 0 has the essential singularity of the form $\exp[-(const)h^{-D/3}]$ (where 1<D<4 is the space dimensionality). It is demonstrated that in terms of the replica formalism this contribution to the free energy comes due to off-perturbative replica …
We study the critical behavior of the three-dimensional $\pm J$ Ising model [with a random-exchange probability $P(J_{xy}) = p δ(J_{xy} - J) + (1-p) δ(J_{xy} + J)$] at the transition line between the paramagnetic and ferromagnetic phase, which extends from $p=1$ to a multicritical (Nishimori) point at $p=p_N\approx 0.767$. By a finite-size scaling analysis of Monte Carlo simulations at various values of $p$ in the region $p_N<p<1$, we provide strong numerical evidence that the critical behavior along the ferromagnetic transition line belongs to the same universality class as the three-dimensio…
We study the $\pm J$ three-dimensional Ising model with a spatially uniaxially anisotropic bond randomness on the simple cubic lattice. The $\pm J$ random exchange is applied in the $xy$ planes, whereas in the z direction only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied, at the ferromagnetic-paramagnetic transition line, using parallel tempering and a convenient concentration of antiferromagnetic bonds ($p_z=0 ; p_{xy}=0.176$). The numerical data point out clearly to a second-order ferromagnet…
We review the value of the critical exponents $ν^{-1}$, $β/ν$, and $γ/ν$ of ferromagnetic Ising model on fractal lattices of Hausdorff dimension between one and three. They are obtained by Monte Carlo simulation with the help of Wolff algorithm. The results are accurate enough to show that the hyperscaling law $d_f=2β/ν+γ/ν$ is satisfied in non-integer dimension. Nevertheless, the discrepancy between the simulation results and the $ε$-expansion studies suggests that the strong universality should be adapted for the fractal lattices.
It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on the strength of the random coupling for strongly disordered cases. Monte Carlo measurements of thermodynamic (infinite volume limit) data of the correlation length ($ξ$) up to $ξ\simeq 200$ along with measurements of the fourth order cumulant ratio (Binder's ratio) at criticality are reported and analyzed in view of two competing scenarios. It is demonstrate…
