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<p>We consider, in any dimension, a constrained lattice gas introduced by physicists [<CitationRef CitationID="CR1">1</CitationRef>], which is an exclusion process on a <i>d</i>-dimensional lattice following the additional constraint that only particles with at least one occupied neighbour can jump. In dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(d\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, 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 [<CitationRef CitationID="CR2">2</CitationRef>].</p>

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Scaling Relations for the CLG’s Critical Exponents

  • 期刊论文

  • 发表日期：

    2026年7月21日

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  • Clément Erignoux,
  • Assaf Shapira,
  • Marielle Simon

摘要

We consider, in any dimension, a constrained lattice gas introduced by physicists [1], 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 \(d\ge 2\) 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 [2].