Non-Robustness of the Zero-Temperature-Limit Gibbs Measures to Perturbations of the Potential
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911074755805184 |
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| author | Gayral, Léo Sablik, Mathieu |
| author_facet | Gayral, Léo Sablik, Mathieu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Robustness of the Zero-Temperature-Limit Gibbs Measures to Perturbations of the Potential Gayral, Léo Sablik, Mathieu Mathematical Physics Statistical Mechanics Combinatorics Dynamical Systems 82B20, 37D35, 68Q17 (Primary) 68Q04, 68Q87, 37B51, 05B45 (Secondary) 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. |
| title | Non-Robustness of the Zero-Temperature-Limit Gibbs Measures to Perturbations of the Potential |
| topic | Mathematical Physics Statistical Mechanics Combinatorics Dynamical Systems 82B20, 37D35, 68Q17 (Primary) 68Q04, 68Q87, 37B51, 05B45 (Secondary) |
| url | https://arxiv.org/abs/2507.18325 |