Order-disorder transition in a model with two symmetric absorbing states

TL;DR

This paper investigates a two-dimensional interacting monomer model with two symmetric absorbing states, demonstrating that its order-disorder transition belongs to the Ising universality class through various finite-size scaling analyses.

Contribution

It provides evidence that the order-disorder transition in models with symmetric absorbing states is in the Ising universality class, challenging recent claims and highlighting the limitations of the Binder cumulant.

Findings

The transition follows Ising critical exponents.

Binder cumulant can mislead critical point estimation.

Model's behavior supports universality hypothesis.

Abstract

We study a model of two-dimensional interacting monomers which has two symmetric absorbing states and exhibits two kinds of phase transition; one is an order-disorder transition and the other is an absorbing phase transition. Our focus is around the order-disorder transition, and we investigate whether this transition is described by the critical exponents of the two-dimensional Ising model. By analyzing the relaxation dynamics of "staggered magnetization," the finite-size scaling, and the behavior of the magnetization in the presence of a symmetry-breaking field, we show that this model should belong to the Ising universality class. Our results along with the universality hypothesis support the idea that the order-disorder transition in two-dimensional models with two symmetric absorbing states is of the Ising universality class, contrary to the recent claim [K. Nam et al., J. Stat. Mech.: Theory Exp. (2011) L06001]. Furthermore, we illustrate that the Binder cumulant could be a misleading guide to the critical point in these systems.