We investigate the critical dynamics of a classical ferromagnet on the simple cubic lattice with doubleexchange interaction. Estimates for the dynamic critical exponents z and are obtained using short-time Monte Carlo simulations. We also estimate the static critical exponents and ␤ studying the behavior of the samples at an early time. Our results are in good agreement with available estimates and support the assertion that this model and the classical Heisenberg model belong to the same universality class.

By using an appropriate version of the synchronous SIR model, we studied the effects of dilution and mobility on the critical immunization rate. We showed that, by applying time-dependent Monte Carlo (MC) simulations at criticality, and taking into account the optimization of the power law for the density of infected individuals, the critical immunization necessary to block the epidemic in two-dimensional lattices decreases as dilution increases with a logarithmic dependence. On the other hand, the mobility minimizes such effects and the critical immunizations is greater when the probability of movement of the individuals increases.

In this paper we revisited the Ziff-Gulari-Barshad model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We use a method proposed recently to locate the nonequilibrium second-order phase transitions and that has been successfully used in systems with defined Hamiltonians and with absorbing states. This method, which is based on optimization of the coefficient of determination of the order parameter, was able to characterize the continuous phase transition of the model, as well as its upper spinodal point, a pseudocritical point located near the discontinuous phase transition. The static critical exponents β, ν_{∥}, and ν_{⊥}, as well as the dynamic critical exponents θ and z for the continuous transition point, were also estimated and are in excellent agreement with results found in literature.

We have investigated the dynamic critical behavior of the two-dimensional Z(5)-symmetric spin model by using short-time Monte Carlo (MC) simulations. We have obtained estimates of some critical points in its rich phase diagram and included, among the usual critical lines the study of first-order (weak) transition by looking into the order-disorder phase transition. Besides, we also investigated the soft-disorder phase transition by considering empiric methods. A study of the behavior of β/νz along the self-dual critical line has been performed and special attention has been devoted to the critical bifurcation point, or FZ (Fateev-Zamolodchikov) point. Firstly, by using a refinement method and taking into account simulations out-of-equilibrium, we were able to localize parameters of this point. In a second part of our study, we turned our attention to the behavior of the model at the early stage of its time evolution in order to find the dynamic critical exponent z as well as the static critical exponents β and ν of the FZ-point on square lattices. The values of the static critical exponents and parameters are in good agreement with the exact results, and the dynamic critical exponent z ≈ 2.28 very close of the 4-state Potts model (z ≈ 2.29).