J. R. Drugowich de Felicio

Mixed initial conditions to estimate the dynamic critical exponent in short-time Monte Carlo simulation

We explore the initial conditions in short-time critical dynamics to propose an alternative way to evaluate the dynamic exponent z. Estimates are obtained with high precision for the 2D Ising model and the 2D Potts model with three and four states by performing heat-bath Monte Carlo simulations.

Universality and scaling study of the critical behavior of the two-dimensional Blume-Capel model in short-time dynamics

In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the magnetization and its moments at an early stage of the dynamic evolution. Our estimates for the dynamic exponents, at the tricritical point, are z=2.215(2) and theta=-0.53(2).

Short-time critical dynamics of the Baxter-Wu model

We study the early time behavior of the Baxter-Wu model, an Ising model with three-spin interactions on a triangular lattice. Our estimates for the dynamic exponent z are compatible with results recently obtained for two models which belong to the same universality class of the Baxter-Wu model: the two-dimensional four-state Potts model and the Ising model with three-spin interactions in one direction. However, our estimates for the dynamic exponent theta of the Baxter-Wu model are completely different from the values obtained for those models. This discrepancy could be related to the absence of a marginal operator in the Baxter-Wu model.

Global persistence exponent of the two-dimensional Blume-Capel model

The global persistence exponent theta(g) is calculated for the two-dimensional Blume-Capel model following a quench to the critical point from both disordered states and such with small initial magnetizations. Estimates are obtained for the nonequilibrium critical dynamics on the critical line and at the tricritical point. Ising-like universality is observed along the critical line and a different value theta(g)=1.080(4) is found at the tricritical point.

An alternative order parameter for the 4-state potts model

We have investigated the dynamic critical behavior of the two-dimensional 4-state Potts model using an alternative order parameter first used by Vanderzande [J. Phys. A 20 (1987) L549] in the study of the Z(5) model. We have estimated the global persistence exponent θg by following the time evolution of the probability P(t) that the considered order parameter does not change its sign up to time t. We have also obtained the critical exponents θ, z, ν, and β using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature.

DYNAMIC CRITICAL EXPONENTS OF THE ISING MODEL WITH MULTISPIN INTERACTIONS

We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents z, θ, β and ν. Taking properly into account the symmetry of the Hamiltonian, we obtain results completely different from those obtained by Wang et al.10 For the dynamic exponent z our result coincides with that of the 4-state Potts model in two dimensions. In addition, results for the static exponents ν and β agree with previous estimates obtained from finite size scaling combined with conformal invariance. Finally, for the new dynamic exponent θ we find a negative and close to zero value, a result also expected for the 4-state Potts model according to Okano et al.

Critical behavior of nonequilibrium models in short-time Monte Carlo simulations.

We analyze two alternative methods for determining the dynamic critical exponent z of the contact process and the Domany-Kinzel cellular automaton in Monte Carlo simulations. One method employs mixed initial conditions, as proposed for magnetic models [Phys. Lett. A 298, 325 (2002)]]; the other is based on the growth of the moment ratio m (t) = /2 starting with all sites occupied. The methods provide reliable estimates for z using the short-time dynamics of the process. Estimates of nu|| are obtained using a method suggested by Grassberger.

Critical behavior of a probabilistic cellular automaton describing a biological system.

We study nonequilibrium phase transitions occurring in a probabilistic cellular automaton which describes one part of the immune system. In this model, each site can be occupied by three type of cells and the immune response under parasitic infections is described in terms of two parameters p and r. The local rules governing the evolution of this automaton possess “up–down” symmetry similar to Ising models. Performing Monte Carlo simulations on square and cubic lattices we verify that the model displays continuous kinetic phase transitions with spontaneous symmetry breaking. We present detailed simulations and analysis of the critical behavior. Our results indicate that the model belongs to the Ising universality class, supporting the “up–down” conjecture.

Global persistence exponent of the double-exchange model.

We obtained the global persistence exponent for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent theta(g) by following the time evolution of probability P(t) that the order parameter of the model does not change its sign up to time t[P(t) approximately t(-theta(g)]. Afterwards, that exponent was estimated through the scaling collapse of the universal function L(theta(g)(z)P(t) for different lattice sizes. Our results for both approaches are in very good agreement with each other.

Short-time behavior of a classical ferromagnet with double-exchange interaction

We investigate the critical dynamics of a classical ferromagnet on the simple cubic lattice with double-exchange interaction. Estimates for the dynamic critical exponents