Moment ratios for the pair contact process with diffusion

TL;DR

This paper investigates the critical behavior of the one-dimensional pair contact process with diffusion, focusing on moment ratios and finite-size effects, and compares findings with directed percolation.

Contribution

The study provides detailed moment ratio analysis at the critical point for large systems and offers an improved estimate for the nondiffusive process.

Findings

Moment ratios converge only at large system sizes due to finite-size effects.

Comparison of moment ratios with directed percolation reveals differences.

An improved critical point estimate for the nondiffusive process is provided.

Abstract

We study the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). In previous studies [Dickman and de Menezes, Phys. Rev. E, 66 045101(R) (2002)], the critical point moment ratios of the order parameter showed anomalous behavior, growing with system size rather than taking universal values, as expected. Using the quasistationary simulation method we determine the moments of the order parameter up to fourth order at the critical point, in systems of up to 40960 sites. Due to strong finite-size effects, the ratios converge only for large system sizes. Moment ratios and associated order-parameter histograms are compared with those of directed percolation. We also report an improved estimate [p_c =0.077092(1)] for the nondiffusive pair contact process.