Crossover from the parity-conserving pair contact process with diffusion to other universality classes

TL;DR

This paper investigates the critical behavior and universality class crossovers of the pair contact process with diffusion, revealing distinct fixed points and crossover exponents that differentiate it from directed percolation.

Contribution

It demonstrates that the PCPD shares critical behavior with the PCPD, studies its crossover to DI and DP classes, and introduces a new route from PCPD to DP via symmetry breaking.

Findings

Crossover exponent for PCPD to DI is 0.57(3).

Crossover exponent for DP to DI is 0.73(4).

New crossover route from PCPD to DP with exponent 1.23(10).

Abstract

The pair contact process with diffusion (PCPD) with modulo 2 conservation (\pcpdt) [$2A\to 4A$, $2A\to 0$] is studied in one dimension, focused on the crossover to other well established universality classes: the directed Ising (DI) and the directed percolation (DP). First, we show that the \pcpdt shares the critical behaviors with the PCPD, both with and without directional bias. Second, the crossover from the \pcpdt to the DI is studied by including a parity-conserving single-particle process ($A \to 3A$). We find the crossover exponent $1/\phi_1 = 0.57(3)$, which is argued to be identical to that of the PCPD-to-DP crossover by adding $A \to 2A$. This suggests that the PCPD universality class has a well defined fixed point distinct from the DP. Third, we study the crossover from a hybrid-type reaction-diffusion process belonging to the DP [$3A\to 5A$, $2A\to 0$] to the DI by adding $A \to 3A$. We find $1/\phi_2 = 0.73(4)$ for the DP-to-DI crossover. The inequality of $\phi_1$ and $\phi_2$ further supports the non-DP nature of the PCPD scaling. Finally, we introduce a symmetry-breaking field in the dual spin language to study the crossover from the \pcpdt to the DP. We find $1/\phi_3 = 1.23(10)$, which is associated with a new independent route from the PCPD to the DP.