Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain
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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BibTeX
@misc{chalhoub2026delocalisation,
title = {{Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain}},
author = {Christopher Chalhoub and Paul Dario and Corentin Faipeur and Arnaud Le Ny},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18786},
eprint = {2609.18786},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18786},
}
RIS
TY - UNPB
TI - Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain
AU - Christopher Chalhoub
AU - Paul Dario
AU - Corentin Faipeur
AU - Arnaud Le Ny
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18786
UR - https://arxiv.org/abs/2609.18786
AB - 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.
ER -