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

TL;DR

This paper investigates the fragility of low-temperature Gibbs measures in certain statistical physics models, showing that small potential perturbations can lead to significant changes in their behavior.

Contribution

The paper provides a formal mathematical analysis demonstrating that some models' low-temperature Gibbs measures are highly sensitive to potential perturbations, challenging assumptions of robustness.

Findings

Low-temperature Gibbs measures can be highly non-robust to potential perturbations

Certain models exhibit significant behavioral changes under small potential modifications

The study highlights the importance of considering perturbation effects in statistical physics models

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.