Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states

TL;DR

This paper develops a finite size scaling theory for discontinuous nonequilibrium phase transitions into absorbing states, demonstrating that key quantities scale with volume and unifying the understanding of such transitions.

Contribution

It introduces a general finite size scaling framework for nonequilibrium phase transitions into absorbing states, supported by simulations of diverse lattice models.

Findings

Quantities scale with volume, enabling thermodynamic limit estimates.

Quasi-stationary simulation methods effectively analyze absorbing phase transitions.

Unified scaling behavior observed across different models and transition types.

Abstract

Based on quasi-stationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as, response functions, cumulants, and equal area probability distributions, all scale with the volume, thus allowing proper estimates for the thermodynamic limit. To illustrate these results, five very distinct lattice models displaying nonequilibrium transitions -- to single and infinitely many absorbing states -- are investigated. The innate difficulties in analyzing absorbing phase transitions are circumvented through quasi-stationary simulation methods. Our findings (allied to numerical studies in the literature) strongly point to an unifying discontinuous phase transition scaling behavior for equilibrium and this important class of nonequilibrium systems.