A planar Ising model of self-organized criticality

• 成果类型: Article
• 署名作者: Forien, Nicolas
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01025-9
• 发表日期: 2021
• 页码: 163-198
• 关键词: abelian sandpile; inequalities; percolation; crystal

摘要

We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the system towards the critical point. Using the finite-size scaling results of Cerf and Messikh (Theory Relat Fields 150(1-2):193-217, 2011. ), we show that, when the size of the box grows to infinity, the temperature concentrates around the critical temperature of the planar Ising model on the square lattice.