On the critical behavior of the one dimensional, diffusive pair contact process

TL;DR

This paper investigates the phase transition behavior of the one-dimensional diffusive pair contact process using cluster mean-field approximations and high-precision simulations, revealing nuanced insights into its critical exponents and class distinctions.

Contribution

It provides new high-precision simulation data and cluster mean-field analysis that clarify the critical behavior and class distinctions of the PCPD.

Findings

Cluster approximations show smooth transition lines with beta_2=2.

Simulation data suggest a narrower gap between different class exponents.

Possibility of a single universality class with logarithmic corrections is supported.

Abstract

The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N=3,4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate D with beta_2=2 mean-field order parameter exponent of the pair density. This contradicts with former N=2 results, where two different mean-field behavior was found along the transition line. Extensive dynamical simulations on L=10^5 lattices give estimates for the order parameter exponents of the particles for 0.05 <= D <= 0.7. These data can support former two distinct class findings. However the gap between low and high D exponents is narrower than estimated previously and the possibility for interpreting numerical data as a single class behavior with exponents alpha=0.21(1), beta=0.41(1) assuming logarithmic corrections is shown. Finite size scaling and cluster simulation results are also presented.