Non-Robustness of the Zero-Temperature-Limit Gibbs Measures to Perturbations of the Potential

2025/07/24 by Léo Gayral, Mathieu Sablik, Gayral, Léo +1
Physics and Astronomy · #05B45 (Secondary) #37B51 #37D35 #68Q17 (Primary) 68Q04 #68Q87 #82B20 #Advanced Thermodynamics and Statistical Mechanics #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2507.18325

openalex publication_date 2025/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The robustness of properties of a statistical physics model to slight perturbations in the exact local interactions of the model is a very relevant philosophical question, considering real-life measurements on which we base some models can only ever reach a finite precision. In this article, we will discuss this topic in a formal mathematical setting, and notably exhibit a family of models for which the low-temperature behaviour is highly non-robust.

Citations

• Freezing Phase Transitions for Lattice Systems and Higher-Dimensional Subshifts
• Characterisation of the Set of Ground States of Uniformly Chaotic Finite-Range Lattice Models
• Pentaplexity A Class of Non-Periodic Tilings of the Plane

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