Critical phenomena in presence of symmetric absorbing states: a microscopic spin model with tunable parameters

TL;DR

This paper introduces a microscopic spin model with tunable parameters that replicates the critical phenomena and universality classes predicted by Langevin descriptions for systems with symmetric absorbing states, confirmed through extensive simulations.

Contribution

The authors present a new microscopic spin model with continuously adjustable parameters that captures the critical behavior and universality classes of symmetric absorbing state systems.

Findings

The model reproduces the phase diagram with three phases and critical lines in three universality classes.

The Ising and directed percolation lines merge into a generalized voter line in the model.

Time-dependent critical quantities exhibit complex behavior in the generalized voter universality class.

Abstract

The Langevin description of systems with two symmetric absorbing states yields a phase diagram with three different phases (disordered and active, ordered and active, absorbing) separated by critical lines belonging to three different universality classes (generalized voter, Ising, and directed percolation). In this paper we present a microscopic spin model with two symmetric absorbing states that has the property that the model parameters can be varied in a continuous way. Our results, obtained through extensive numerical simulations, indicate that all features of the Langevin description are encountered for our two-dimensionsal microscopic spin model. Thus the Ising and direction percolation lines merge into a generalized voter critical line at a point in parameter space that is not identical to the classical voter model. A vast range of different quantities are used to determine the universality classes of the order-disorder and absorbing phase transitions. The investigation of time-dependent quantities at a critical point belonging to the generalized voter universality class reveals a more complicated picture than previously discussed in the literature.