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.
Categories: math-ph cond-mat.stat-mech math.CO math.DS math.MP