Identifying universality classes of absorbing phase transitions by block renormalization

TL;DR

This paper introduces a block renormalization method to reliably identify universality classes of absorbing phase transitions by analyzing universal probability ratios of block states.

Contribution

It develops a renormalization scheme based on block-spin ideas to distinguish universality classes through universal probability ratios at criticality.

Findings

Universal probability ratios serve as fingerprints for universality classes.

The method reliably classifies absorbing phase transitions.

Large block size measurements reveal universal constants.

Abstract

We propose a renormalization scheme that can be used as a reliable method to identify universality classes of absorbing phase transitions. Following the spirit of Wilson's block-spin renormalization group, the lattice is divided into blocks, assigning to them an effective state by a suitable Boolean function of the interior degrees of freedom. The effective states of adjacent blocks form certain patterns which are shown to occur with universal probability ratios if the underlying process is critical. Measuring these probability ratios in the limit of large block sizes one obtains a set of universal numbers as an individual fingerprint for each universality class.