Block scaling in the directed percolation universality class

TL;DR

This paper investigates the block (finite size) scaling behavior of the order parameter in the directed percolation universality class, highlighting the influence of ensemble choice and uncovering unconventional scaling phenomena.

Contribution

It provides a detailed analysis of how ensemble selection affects block scaling and reveals unconventional power-law dependencies in the unconditional ensemble.

Findings

Conditional ensemble exhibits expected block-scaling behavior.

Unconditional ensemble shows unconventional power-law scaling.

Ensemble choice impacts the scaling functions and symmetry properties.

Abstract

The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its fluctuations, considering (sub-)blocks of linear size l in systems of linear size L. The scaling depends on the choice of the ensemble, as only the conditional ensemble produces the block-scaling behaviour as established in equilibrium critical phenomena. The dependence on the ensemble can be understood by an additional symmetry present in the unconditional ensemble. The unconventional scaling found in the unconditional ensemble is a reminder of the possibility that scaling functions themselves have a power-law dependence on their arguments.