Dynamic behavior of driven interfaces in models with two absorbing states

TL;DR

This paper investigates the dynamics of interfaces in models with two absorbing states, revealing how symmetry-breaking influences interface behavior and the transition between universality classes.

Contribution

It provides a detailed analysis of driven interface behavior in models with two absorbing states, including the effects of symmetry-breaking fields and crossover phenomena.

Findings

Interface spreads ballistically in the active phase.

Spreading velocity vanishes algebraically at criticality.

Discontinuous jump in spreading velocity at the transition.

Abstract

We study the dynamics of an interface (active domain) between different absorbing regions in models with two absorbing states in one dimension; probabilistic cellular automata models and interacting monomer-dimer models. These models exhibit a continuous transition from an active phase into an absorbing phase, which belongs to the directed Ising (DI) universality class. In the active phase, the interface spreads ballistically into the absorbing regions and the interface width diverges linearly in time. Approaching the critical point, the spreading velocity of the interface vanishes algebraically with a DI critical exponent. Introducing a symmetry-breaking field $h$ that prefers one absorbing state over the other drives the interface to move asymmetrically toward the unpreferred absorbing region. In Monte Carlo simulations, we find that the spreading velocity of this driven interface shows a discontinuous jump at criticality. We explain that this unusual behavior is due to a finite relaxation time in the absorbing phase. The crossover behavior from the symmetric case (DI class) to the asymmetric case (directed percolation class) is also studied. We find the scaling dimension of the symmetry-breaking field $y_h = 1.21(5)$.