Critical behavior in lattice models with two symmetric absorbing state

TL;DR

This paper investigates phase transitions in lattice models with two symmetric absorbing states, revealing their universality classes and critical behavior through mean-field and numerical methods.

Contribution

It provides a detailed analysis of the phase diagram and critical points of models with two symmetric absorbing states, identifying universality classes and scaling behavior.

Findings

Transition between paramagnetic and ferromagnetic phases belongs to Ising universality class.

Transition between ferromagnetic and absorbing phases belongs to directed percolation class.

The ferromagnetic phase size vanishes linearly with the distance to the voter point.

Abstract

We analyze nonequilibrium lattice models with up-down symmetry and two absorbing states by mean-field approximations and numerical simulations in two and three dimensions. The phase diagram displays three phases: paramagnetic, ferromagnetic and absorbing. The transition line between the first two phases belongs to the Ising universality class and between the last two, to the direct percolation universality class. The two lines meet at the point describing the voter model and the size $\ell$ of the ferromagnetic phase vanishes with the distance $\varepsilon$ to the voter point as $\ell\sim\varepsilon$, with possible logarithm corrections in two dimensions.