发表机构
Imperial College London; CY Cergy Paris Université; UPEC（帝国理工学院; 塞吉-巴黎西大学; 巴黎十二大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究无序长程离散高斯链在随机场下的离域化，证明对α>3/2任意温度离域，并给出增长指数与标度极限。
AI 中文摘要
本文研究了外部随机场对长程离散高斯链（DGC）局域化/离域化的影响，该模型近期由Garban（arXiv:2312.04536）和Coquille等人（arXiv:2412.15782）研究。我们证明，对于任何多项式衰减指数α > 3/2，该模型在任意逆温度下都是离域化的。这一行为与无无序长程DGC的行为有本质区别，后者仅在α > 2时才能在任意温度下离域化，这与Aizenman和Wehr已证明的长程Ising模型的情况类似。此外，我们通过确定任意衰减指数α > 3/2下原点高度的增长指数和标度极限，提供了离域化相更详细的描述。
英文摘要
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 $α> 3/2$.
Comments45 pages, 3 figures
