Hyperscaling relations in the bosonic pair contact process with diffusion

TL;DR

This paper investigates hyperscaling relations in the bosonic pair contact process with diffusion, analyzing critical exponents and phase transitions through spreading dynamics from an initial seed.

Contribution

It provides an exact determination of some critical exponents and tests hyperscaling relations in a bosonic contact process with diffusion, highlighting unique properties of this absorbing phase transition.

Findings

Autocorrelation function exhibits a phase transition at the critical point.

Some critical exponents can be determined exactly.

Numerical data production is challenging in certain cases.

Abstract

A hyperscaling relation for the critical exponents of absorbing phase transitions is tested in the bosonic pair contact process with diffusion. To this end spreading is considered, i.e. the time evolution out of an initial seed. It is shown that like in the case of spatial homogeneous initial conditions the autocorrelation function exhibits a phase transition at the critical point of the first moment. Some of the critical exponents can be determined exactly which is an unusual property of an absorbing phase transition and provides a possibility to test the hyperscaling relation. In the case of the bosonic pair contact process with diffusion three sets of exponents can be considered referring to the number of particles, number of pairs and number of active sites. It is argued that in special cases it is generally impossible to produce adequate data numerically.