Nonuniversality in the pair contact process with diffusion

TL;DR

This paper investigates the one-dimensional pair contact process with diffusion, revealing nonuniversal critical exponents, a violation of scaling, and identifying a universal moment ratio value in the parity-conserving class.

Contribution

It demonstrates the nonuniversality of critical exponents with diffusion rate and identifies a universal moment ratio in the parity-conserving class.

Findings

Critical exponents vary with diffusion rate.

Order-parameter moment ratio grows logarithmically with system size.

Universal moment ratio m_c = 1.334 confirmed for the parity-conserving class.

Abstract

We study the static and dynamic behavior of the one dimensional pair contact process with diffusion. Several critical exponents are found to vary with the diffusion rate, while the order-parameter moment ratio m=\bar{rho^2} /\bar{rho}^2 grows logarithmically with the system size. The anomalous behavior of m is traced to a violation of scaling in the order parameter probability density, which in turn reflects the presence of two distinct sectors, one purely diffusive, the other reactive, within the active phase. Studies restricted to the reactive sector yield precise estimates for exponents beta and nu_perp, and confirm finite size scaling of the order parameter. In the course of our study we determine, for the first time, the universal value m_c = 1.334 associated with the parity-conserving universality class in one dimension.