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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Short-time dynamics of a metamagnetic model

M. Santos, W. Figueiredo

Published Aug 1, 2000• 11 citations
Publisher

Abstract

We studied a layered metamagnetic Ising model with competing ferromagnetic and antiferromagnetic interactions on a square lattice. The model is formed of ferromagnetic chains coupled by an antiferromagnetic interaction. Using Monte Carlo simulations we have determined the phase diagram of the model, which exhibits a tricritical point. By exploring the short-time scaling dynamics, we have found the dynamic and static critical exponents along the continuous transition line between the antiferromagnetic and paramagnetic phases.

DOI
10.1103/physreve.62.1799

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We studied a layered metamagnetic Ising model with competing ferromagnetic and antiferromagnetic interactions on a square lattice. The model is formed of ferromagnetic chains coupled by an antiferromagnetic interaction. Using Monte Carlo simulations we have determined the phase diagram of the model, which exhibits a tricritical point. By exploring the short-time scaling dynamics, we have found the dynamic and static critical exponents along the continuous transition line between the antiferromagnetic and paramagnetic phases.
Using the parallel tempering algorithm and graphics processing unit accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor and next-nearest-neighbor interactions of the same strength and subject to a uniform magnetic field. Both transitions from the (2x1) and row-shifted (2x2) ordered phases to the paramagnetic phase are continuous. From our data analysis, re-entrance behavior of the (2x1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the critical exponents we obtained along the phase boundary, Suzuki's weak universality seems to hold.
In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width nnn (hn)({h}_{n})(hn​) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants $\ensuremath{\delta}$. The obtained results indicate that the h1{h}_{1}h1​-TL phase transition line is continuous up to $\ensuremath{\delta}=1.2585$, while for the h2{h}_{2}h2​-TL line a weak first-order character is found in the interval $1.2585\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}1.36$ and becomes continuous for $1.37\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}1.9$. This result suggests the existence of a tricritical point close to $\ensuremath{\delta}=1.37$. When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on $\ensuremath{\delta}$ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the ${h}_{1}\ensuremath{-}{h}_{2}$ line, i.e., at $\ensuremath{\delta}=1.2585$, the critical phase corresponding to the ${h}_{1}\ensuremath{-}\mathrm{TL}$ transition coexists with the h2{h}_{2}h2​ phase.
We investigated the dynamical behavior of an Ising model in a square lattice subject to a time-dependent external magnetic field. In our model the exchange coupling between first neighboring spins in the horizontal direction is different from that of the vertical direction. We have employed the master equation approach for the Glauber stochastic process and used the dynamical pair approximation in order to decouple the hierarchy of equations. We have found the stationary phase diagram for this model in the plane amplitude of the oscillating field versus temperature, for different values of the frequency of the external field and of the ratio between the vertical and the horizontal couplings. Depending on these values, the phase diagram can exhibit the ferromagnetic, paramagnetic, and antiferromagnetic phases. The transition between these phases can be continuous or discontinuous, and the model may also display a tricritical behavior.
The critical relaxation from the low-temperature ordered state of the three-dimensional Ising model with competing interactions on a simple cubic lattice has been studied for the first time using the short-time dynamics method. Competition between exchange interactions is due to the ferromagnetic interaction between the nearest neighbors and the antiferromagnetic interaction between the next nearest neighbors. Particles containing 262144 spins with periodic boundary conditions have been studied. Calculations have been performed by the standard Metropolis Monte Carlo algorithm. The static critical exponents of the magnetization and correlation radius have been calculated. The dynamic critical exponent of the model under study has been calculated for the first time.
We employed Monte Carlo simulations and short-time dynamic scaling to determine the static and dynamic critical exponents for the generalized two-dimensional Blume-Capel model of spin-3/2. We showed that the critical behavior at the second-order phase-transition line between the paramagnetic and ferromagnetic phases is in the same universality class of the two-dimensional Ising model. However, at the double critical end point, which is present in the phase diagram of the model, the critical exponent beta , associated to the order parameter, is different from that of the Ising model.
We have performed large-scale numerical simulations for the ± J Ising model on the simple cubic and the square lattices with asymmetric weight of ferromagnetic and antiferromagnetic bonds. The Monte Carlo renormalization group method is used to estimate T c , γ/ν, β/ν and ν at various points along the phase boundary between ferromagnetic and paramagnetic phases including the tricritical point. The obtained values of T c and the resulting phase diagrams of the simple cubic and the square lattices are much more accurate than those estimated so far. In the simple cubic lattice, we find evidence for the possibility that universality of the ferromagnetic critical exponents holds along the critical line except at the tricritical point, while weak universality holds even at the tricritical point. Weak universality seems to hold also in the square lattice.