Critical phenomena of nonequilibrium dynamical systems with two absorbing states

TL;DR

This paper investigates how symmetry-breaking affects the universality class of nonequilibrium systems with two absorbing states, revealing that symmetry plays a crucial role over conservation laws in determining critical behavior.

Contribution

It demonstrates that breaking the symmetry between absorbing states shifts the universality class from parity-conserving to directed percolation, highlighting the importance of symmetry in critical phenomena.

Findings

Symmetry-breaking causes the system to revert to directed percolation universality class.

Interface dynamics exhibit new universal exponents and trivial scaling with symmetry-breaking.

Hyperscaling relation is restored when focusing on the interface near the preferred absorbing state.

Abstract

We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit a continuous phase transition from an active phase into an absorbing phase which belongs to the universality class of the models with the parity conservation. However, when we break the symmetry between the absorbing states by introducing a symmetry-breaking field, Monte Carlo simulations show that the system goes back to the conventional directed percolation universality class. In terms of domain wall language, the parity conservation is not affected by the presence of the symmetry-breaking field. So the symmetry between the absorbing states rather than the conservation laws plays an essential role in determining the universality class. We also perform Monte Carlo simulations for the various interface dynamics between different absorbing states, which yield new universal dynamic exponents. With the symmetry-breaking field, the interface moves, in average, with a constant velocity in the direction of the unpreferred absorbing state and the dynamic scaling exponents apparently assume trivial values. However, we find that the hyperscaling relation for the directed percolation universality class is restored if one focuses on the dynamics of the interface on the side of the preferred absorbing state only.