Some recent developments in models with absorbing states

TL;DR

This paper reviews recent advances in models with absorbing states, including the nonequilibrium Potts model, effects of interactions on critical behavior, and connections to synchronization and interfacial models.

Contribution

It introduces new findings on how interactions influence critical points and explores the relationship between synchronization transitions and interfacial models.

Findings

Further neighbour interactions can split the voter critical point in 2D.

Synchronization transition relates to interfacial models.

Critical behavior is affected by factors like interactions and system dimensionality.

Abstract

We describe some of the recent results obtained for models with absorbing states. First, we present the nonequilibrium absorbing-state Potts model and discuss some of the factors that might affect the critical behaviour of such models. In particular we show that in two dimensions the further neighbour interactions might split the voter critical point into two critical points. We also describe some of the results obtained in the context of synchronization of chaotic dynamical systems. Moreover, we discuss the relation of the synchronization transition with some interfacial models.