Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results

TL;DR

This paper provides exact results on phase transitions and correlation behaviors in the bosonic pair contact process with diffusion, revealing how diffusion constants influence variance divergence and correlation properties at criticality.

Contribution

It offers an exact analysis of the variance and correlation functions in the PCPD with diffusion, highlighting the role of diffusion constants in phase transition behavior.

Findings

Variance approaches a finite value for high diffusion constants in d>2

Variance diverges exponentially for low diffusion constants

Dynamical scaling with exponent z=2 is observed

Abstract

The variance of the local density of the pair contact process with diffusion (PCPD) is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is shown that for lattice dimension d>2 the variance exhibits a phase transition: For high enough diffusion constants, it asymptotically approaches a finite value, while for low diffusion constants the variance diverges exponentially in time. This behavior appears also in the density correlation function, implying that the correlation time is negative. Yet one has dynamical scaling with a dynamical exponent calculated to be z=2.