Surface Critical Behavior in Systems with Non-Equilibrium Phase Transitions

TL;DR

This paper investigates the surface critical behavior of non-equilibrium phase transition systems like BARW and DP, revealing differences from mean field predictions, especially in lower dimensions, and identifying unique surface exponents.

Contribution

It provides a detailed analysis of surface critical phenomena in BARW and DP, including new surface exponents and duality relations, especially below the upper critical dimension.

Findings

Surface phase diagrams differ significantly from mean field predictions in low dimensions.

Two independent surface beta_1 exponents are identified in 1D BARW.

Monte Carlo simulations support many theoretical predictions.

Abstract

We study the surface critical behavior of branching-annihilating random walks with an even number of offspring (BARW) and directed percolation (DP) using a variety of theoretical techniques. Above the upper critical dimensions d_c, with d_c=4 (DP) and d_c=2 (BARW), we use mean field theory to analyze the surface phase diagrams using the standard classification into ordinary, special, surface, and extraordinary transitions. For the case of BARW, at or below the upper critical dimension, we use field theoretic methods to study the effects of fluctuations. As in the bulk, the field theory suffers from technical difficulties associated with the presence of a second critical dimension. However, we are still able to analyze the phase diagrams for BARW in d=1,2, which turn out to be very different from their mean field analog. Furthermore, for the case of BARW only (and not for DP), we find two independent surface beta_1 exponents in d=1, arising from two distinct definitions of the order parameter. Using an exact duality transformation on a lattice BARW model in d=1, we uncover a relationship between these two surface beta_1 exponents at the ordinary and special transitions. Many of our predictions are supported using Monte-Carlo simulations of two different models belonging to the BARW universality class.