Scaling Relations For The CLG's Critical Exponents

TL;DR

This paper develops a mathematical framework for scaling relations of critical exponents in a constrained lattice gas model exhibiting self-organized criticality in higher dimensions.

Contribution

It provides a rigorous theoretical foundation for the scaling relations between critical exponents previously observed numerically.

Findings

Derivation of scaling relations between critical exponents.

Mathematical validation of numerical predictions.

Framework applicable to high-dimensional exclusion processes.

Abstract

We consider, in any dimension, the constrained lattice gas introduced by Rossi et al., which is an exclusion process on a d-dimensional lattice following the additional constraint that only particles with at least one occupied neighbour can jump. In dimension d > 2, this model features self-organized criticality at some critical density of particles. Numerical simulations predict the existence of scaling exponents close to criticality, and several relations can be derived between these exponents. The goal of this article is to give a mathematical framework for these relations, which have been numerically established in a companion article.