Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles

TL;DR

This paper investigates how spatial bias affects a nonequilibrium phase transition in a lattice system of coagulating and fragmenting particles, showing that bias inhibits the transition in one dimension but not in two.

Contribution

It analytically demonstrates the suppression of the phase transition by spatial bias in one dimension and analyzes finite size effects, supported by numerical simulations.

Findings

Bias inhibits phase transition in 1D in the thermodynamic limit.

Finite size systems still show transition signatures.

Bias is irrelevant in 2D, preserving the transition.

Abstract

We examine the effect of spatial bias on a nonequilibrium system in which masses on a lattice evolve through the elementary moves of diffusion, coagulation and fragmentation. When there is no preferred directionality in the motion of the masses, the model is known to exhibit a nonequilibrium phase transition between two different types of steady states, in all dimensions. We show analytically that introducing a preferred direction in the motion of the masses inhibits the occurrence of the phase transition in one dimension, in the thermodynamic limit. A finite size system, however, continues to show a signature of the original transition, and we characterize the finite size scaling implications of this. Our analysis is supported by numerical simulations. In two dimensions, bias is shown to be irrelevant.