{"title":"Maximum of the Gaussian Interface Model in Random External Fields","authors":"Hironobu Sakagawa","doi":"10.1007/s10955-024-03309-5","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on <span>\\(\\mathbb {R}^{\\Lambda _N}\\)</span>, <span>\\(\\Lambda _N=[-N, N]^d\\cap \\mathbb {Z}^d\\)</span> with Hamiltonian <span>\\(H_N(\\phi )= \\frac{1}{4d}\\sum \\limits _{x\\sim y}(\\phi (x)-\\phi (y))^2 -\\sum \\limits _{x\\in \\Lambda _N}\\eta (x)\\phi (x)\\)</span> and 0-boundary conditions. <span>\\(\\{\\eta (x)\\}_{x\\in \\mathbb {Z}^d}\\)</span> is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable <span>\\(\\eta (x)\\)</span> when <span>\\(d\\ge 5\\)</span>. In particular, we identify the leading order asymptotics of the maximum.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10955-024-03309-5","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on \(\mathbb {R}^{\Lambda _N}\), \(\Lambda _N=[-N, N]^d\cap \mathbb {Z}^d\) with Hamiltonian \(H_N(\phi )= \frac{1}{4d}\sum \limits _{x\sim y}(\phi (x)-\phi (y))^2 -\sum \limits _{x\in \Lambda _N}\eta (x)\phi (x)\) and 0-boundary conditions. \(\{\eta (x)\}_{x\in \mathbb {Z}^d}\) is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable \(\eta (x)\) when \(d\ge 5\). In particular, we identify the leading order asymptotics of the maximum.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.