Crossovers from parity conserving to directed percolation universality

TL;DR

This paper investigates how models with parity-conserving phase transitions crossover to directed percolation universality class under symmetry-breaking perturbations, revealing diverse sub-classes with distinct scaling behaviors.

Contribution

It provides a detailed numerical and mean-field analysis of the crossover mechanisms from parity conserving to directed percolation universality classes, highlighting different crossover operators and resulting sub-classes.

Findings

External symmetry breaking induces crossover to DP class with specific exponents.

Spontaneous particle decay destroys parity conservation, leading to a different DP crossover.

Models exhibit diversity within the DP universality class, with different cluster scaling exponents.

Abstract

The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric absorbing phases (the NEKIMCA and Grassberger's A stochastic cellular automaton) the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation (DP) and the crossover exponent: 1/\phi ~ 0.53(2). In case an even offspringed branching and annihilating random walk model (dual to NEKIMCA) the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the DP class characterized by the crossover exponent: 1/\phi\simeq 0.205(5). The two different kinds of crossover operators can't be mapped onto each other and the resulting models show a diversity within the DP universality class in one dimension. These 'sub-classes' differ in cluster scaling exponents.