Equivalence of conditional and external field ensembles in absorbing state phase transitions

TL;DR

This paper demonstrates that in absorbing state models, the conditional ensemble without external field is equivalent to the unconditional ensemble with a small external field, linking their scaling behaviors and critical properties.

Contribution

It establishes the equivalence between conditional and external field ensembles in absorbing state phase transitions, clarifying their relation near the critical point.

Findings

Conditional ensemble matches unconditional ensemble at small external field

Both ensembles share the same scaling behavior near criticality

The derivation relies on a single established scaling law

Abstract

I comment on the relation between two sampling methods for absorbing state models. It is shown that a certain ensemble without external field conditional to activity coincides with the unconditional ensemble for sufficiently small external field. The actual physical processes involved are identical and the derivation of the identity of the scaling behaviour relies on a single (established) scaling law. While the conditional ensemble by construction does not contain information about the system with large external field, it contains all information about the limit of vanishing external field and about the vicinity of the critical point: Finite size scaling as well as critical scaling in the temperature-like variable or in (small) external field.