How to discriminate easily between Directed-percolation and Manna scaling

TL;DR

This paper presents a simple method to distinguish between the directed-percolation and Manna universality classes by analyzing their different responses to physical boundaries, aiding in resolving discrepancies in self-organized critical systems.

Contribution

The authors propose a novel, efficient approach to differentiate DP and Manna classes based on boundary behavior, improving classification accuracy in critical phenomena.

Findings

DP and Manna classes respond differently to boundaries

The method effectively discriminates between the two classes

It helps resolve existing classification discrepancies

Abstract

Here we compare critical properties of systems in the directed-percolation (DP) universality class with those of absorbing-state phase transitions occurring in the presence of a non-diffusive conserved field, i.e. transitions in the so-called Manna or C-DP class. Even if it is clearly established that these constitute two different universality classes, most of their universal features (exponents, moment ratios, scaling functions,...) are very similar, making it difficult to discriminate numerically between them. Nevertheless, as illustrated here, the two classes behave in a rather different way upon introducing a physical boundary or wall. Taking advantage of this, we propose a simple and fast method to discriminate between these two universality classes. This is particularly helpful in solving some existing discrepancies in self-organized critical systems as sandpiles.