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arXiv · 2609.18786

Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain

Christopher Chalhoub·Paul Dario·Corentin Faipeur·Arnaud Le Ny
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Abstract

In this paper, we study the effect of an external random field on the localisation / delocalisation of the long-range Discrete Gaussian Chain (DGC), recently studied by Garban arXiv:2312.04536 and Coquille \emph{et al.} arXiv:2412.15782. We prove that the model is delocalised at every inverse temperature for any polynomial decay $α> 3/2$. This behaviour differs qualitatively from the one of the disorder-free long-range DGC, for which delocalisation at every temperature occurs only for $α> 2$, similarly to what happens for long-range Ising models as already proved by Aizenman and Wehr. Additionally, we provide a more detailed description of the delocalised phase by identifying the growth exponent and scaling limit of the height at the origin for any decay exponent $α> 3/2$.

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Christopher Chalhoub, Paul Dario, Corentin Faipeur, Arnaud Le Ny. 2026-09-16. Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain. https://arxiv.org/abs/2609.18786

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