Lattice random-field Widom--Rowlinson models

Benedikt Jahnel; Daniel Kamecke; Christof Külske

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arXiv · 2605.18744

Lattice random-field Widom--Rowlinson models

Benedikt Jahnel·Daniel Kamecke·Christof Külske

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Abstract

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.

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Benedikt Jahnel, Daniel Kamecke, Christof Külske. 2026-05-18. Lattice random-field Widom--Rowlinson models. https://arxiv.org/abs/2605.18744

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