Imry-Ma phenomenon for the hard-core model on $\mathbb{Z}^{2}$
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911363636396032 |
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| author | Ventura, Irene Ayuso Chiarini, Leandro Helmuth, Tyler Powell, Ellen |
| author_facet | Ventura, Irene Ayuso Chiarini, Leandro Helmuth, Tyler Powell, Ellen |
| contents | The \emph{Imry-Ma phenomenon} refers to the dramatic effect that disorder can have on first-order phase transitions for two-dimensional spin systems. The most famous example is the absence of a phase transition for the two-dimensional random-field Ising model. This paper establishes that a similar phenomena takes place for the hard-core model, a discrete model of crystallization: arbitrarily weak disorder prevents the formation of a crystal. Our proof of this behaviour is an adaptation of the Aizenman-Wehr argument for the Imry-Ma phenomenon, with the use of internal (spin space) symmetries for spin systems being replaced by the use spatial symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05798 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Imry-Ma phenomenon for the hard-core model on $\mathbb{Z}^{2}$ Ventura, Irene Ayuso Chiarini, Leandro Helmuth, Tyler Powell, Ellen Probability 82B44 (Primary), 82B20, 60K35 (Secondary) The \emph{Imry-Ma phenomenon} refers to the dramatic effect that disorder can have on first-order phase transitions for two-dimensional spin systems. The most famous example is the absence of a phase transition for the two-dimensional random-field Ising model. This paper establishes that a similar phenomena takes place for the hard-core model, a discrete model of crystallization: arbitrarily weak disorder prevents the formation of a crystal. Our proof of this behaviour is an adaptation of the Aizenman-Wehr argument for the Imry-Ma phenomenon, with the use of internal (spin space) symmetries for spin systems being replaced by the use spatial symmetries. |
| title | Imry-Ma phenomenon for the hard-core model on $\mathbb{Z}^{2}$ |
| topic | Probability 82B44 (Primary), 82B20, 60K35 (Secondary) |
| url | https://arxiv.org/abs/2601.05798 |