Short-time critical dynamics of the Baxter-Wu model

Abstract

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.

Nonequilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line

“…For the TSP model, our estimate is also in complete agreement with those ones presently accepted for the model, z = 2.1983(81) [51], obtained from the time evolution of the self-correlation and z = 2.197(3) obtained by mixing moments of the magnetization under different initial conditions [37], F 2 (t). However, our estimate of z m for the FSP model, is larger, but very close to the values recently obtained for that model, z = 2.290(3) [37] and z = 2.294(3) [35], for the Baxter-Wu model [43], z = 2.294 (6), and for the n = 3 Turban model [54], z = 2.292(4), both belonging to the same universality class of the FSP model.…”

“…Among the points we take into account, we include the critical points of the Ising, TSP, and FSP models. The exponents θ gm , θ m , and z m were obtained numerically for the critical points of the two-dimensional Ising model [20,[47][48][49][50], the TSP model [20,37,51,52], and the FSP model [35,37,43,[52][53][54]. These last two exponents, as well as the exponents θ p and z p were calculated for some points on the self-dual critical line of the Ashkin-Teller model by Li et al [55].…”

The threshold of coexistence and critical behaviour of a predator–prey cellular automaton

“…To this end we perform timedependent simulations [19,20,21,22,23,24,25,26,27,28,29,30,31] which allow us to obtain the phase boundaries together with the critical exponents. The scaling analysis of the time-dependent simulations yields a set of dynamic critical exponents and thus the possibility of classification of the models with absorbing states in universality classes.…”

Stochastic dynamics of coupled systems and damage spreading

“…In the study of damage spreading [10,12,15,[18][19][20][21][22][23][24] it has been realized that algorithms that are realization of the same probalistic rules may yield different results for the damage spreading [21,15,22,24], and they usually do. The damage spreading is a procedure through which we may study the sensibility of the time evolution of systems with respect to the initial conditions.…”