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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.18744 |
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| _version_ | 1866910233102647296 |
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| author | Jahnel, Benedikt Kamecke, Daniel Külske, Christof |
| author_facet | Jahnel, Benedikt Kamecke, Daniel Külske, Christof |
| contents | We consider the Widom--Rowlinson model on $\mathbb{Z}^d$ subject to a symmetric i.i.d.\ random field. We prove that for dimensions $d\le 2$ any non-trivial random field leads to an absence of a phase transition. In contrast, in dimensions $d\ge 3$ and for Gaussian random fields, phase-transition behavior of the model is maintained for sufficiently large densities of occupied sites. This extends the general picture known from the classical random-field Ising model to the random-field Widom--Rowlinson model. Following the general proof route of Aizenman--Wehr as well as Ding--Zhuang, our main contribution rests on adequate notions of contours and their associated generalized spin-flip operation to deal with hard-core repulsions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18744 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lattice random-field Widom--Rowlinson models Jahnel, Benedikt Kamecke, Daniel Külske, Christof Probability 60K37, 82B44 We consider the Widom--Rowlinson model on $\mathbb{Z}^d$ subject to a symmetric i.i.d.\ random field. We prove that for dimensions $d\le 2$ any non-trivial random field leads to an absence of a phase transition. In contrast, in dimensions $d\ge 3$ and for Gaussian random fields, phase-transition behavior of the model is maintained for sufficiently large densities of occupied sites. This extends the general picture known from the classical random-field Ising model to the random-field Widom--Rowlinson model. Following the general proof route of Aizenman--Wehr as well as Ding--Zhuang, our main contribution rests on adequate notions of contours and their associated generalized spin-flip operation to deal with hard-core repulsions. |
| title | Lattice random-field Widom--Rowlinson models |
| topic | Probability 60K37, 82B44 |
| url | https://arxiv.org/abs/2605.18744 |