Generalized Scaling for Models with Multiple Absorbing States

TL;DR

This paper introduces a generalized scaling theory for dynamic critical behavior at transitions into absorbing states, accounting for initial configuration-dependent exponents and supported by lattice model simulations.

Contribution

It proposes a new scaling framework that explains nonuniversal critical exponents in systems with multiple absorbing states, extending traditional hyperscaling relations.

Findings

The theory accurately describes variable critical exponents.

Simulations confirm the generalized hyperscaling relation.

Applicable to models with nonunique absorbing states.

Abstract

At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a transition into an absorbing state, which is capable of describing exponents which vary according to the initial configuration. The resulting hyperscaling relation is supported by simulations of two lattice models.