Three different routes from the directed Ising to the directed percolation class

TL;DR

This study investigates the crossover behavior from the directed Ising to the directed percolation class via three routes, characterizing each by a numerical crossover exponent and analyzing their distinct critical properties.

Contribution

It provides a comprehensive numerical analysis of three different crossover routes from the DI to DP classes, including their crossover exponents and underlying mechanisms.

Findings

Crossover exponents: 2.1±0.1 (SB), 4.6±0.2 (CB), 2.9±0.1 (CC)

Distinct critical behaviors for each crossover route

Domain wall analysis explains SB and CB differences

Abstract

Scaling nature of absorbing critical phenomena is well understood for the directed percolation (DP) and the directed Ising (DI) systems. However, a full analysis of the crossover behavior is still lacking, which is of our interest in this study. There are three different routes from the DI to the DP classes by introducing a symmetry breaking field (SB), breaking a modulo 2 conservation (CB), or making channels connecting two equivalent absorbing states (CC). Each route can be characterized by a crossover exponent, which is found numerically as $\phi=2.1\pm 0.1$ (SB), $4.6\pm 0.2$ (CB), and $2.9\pm 0.1$ (CC), respectively. The difference between the SB and CB crossover can be understood easily in the domain wall language, while the CC crossover involves an additional critical singularity in the auxiliary field density with the memory effect to identify itself independent.