Effect of a Mode of Update on Universality Class for Coupled Logistic Maps: Directed Ising to Ising Class

Abstract

Ising model at zero temperature leads to a ferromagnetic state asymptotically. There are two such possible states linked by symmetry, and Glauber–Ising dynamics are employed to reach them. In some stochastic or deterministic dynamical systems, the same absorbing state with [Formula: see text] symmetry is reached. This transition often belongs to the directed Ising (DI) class where dynamic exponents and persistence exponent are different. In asymmetrically coupled sequentially updated logistic maps, the transition belongs to the DI class. We study changes in the nature of transition with an update scheme. Even with the synchronous update, the transition still belongs to the DI class. We also study a synchronous probabilistic update scheme in which each site is updated with the probability [Formula: see text]. The order parameter decays with an exponent [Formula: see text] in this scheme. Nevertheless, the dynamic exponent [Formula: see text] is less than [Formula: see text] even for small values of [Formula: see text] indicating a very slow crossover to the Ising class. However, with a random asynchronous update, we recover [Formula: see text]. In the presence of feedback, synchronous update leads to a transition in the DI universality class which changes to Ising class for synchronous probabilistic update.