A comparative study for the pair-creation contact process using series expansions

TL;DR

This paper compares two perturbative series expansion methods for the pair-creation contact process, highlighting the limitations of supercritical expansions and proposing subcritical series as a more accurate alternative.

Contribution

It introduces a new approach combining one-site creation with pair-creation and demonstrates the effectiveness of subcritical series expansions for this process.

Findings

Supercritical series expansions are ineffective for pair-creation contact process.

Subcritical series expansions provide estimates consistent with numerical simulations.

Adding one-site creation improves supercritical series applicability.

Abstract

A comparative study between two distinct perturbative series expansions for the pair-creation contact process is presented. In contrast to the ordinary contact process, whose supercritical series expansions provide accurate estimates for its critical behavior, the supercritical approach does not work properly when applied to the pair-creation process. To circumvent this problem a procedure is introduced in which one-site creation is added to the pair-creation. An alternative method is the generation of subcritical series expansions which works even for the case of the pure pair-creation process. Differently from the supercritical case, the subcritical series yields estimates that are compatible with numerical simulations.