UNIVERSALITY FOR THE PINNING MODEL IN THE WEAK COUPLING REGIME

• 成果类型: Article
• 署名作者: Caravenna, Francesco; Toninelli, Fabio Lucid; Torri, Niccolo
• 署名单位: University of Milano-Bicocca; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1109
• 发表日期: 2017
• 页码: 2154-2209
• 关键词: DISORDER; polymer; relevance; THEOREMS; limit

摘要

We consider disordered pinning models, when the return time distribution of the underlying renewal process has a polynomial tail with exponent alpha is an element of (1/2, 1). This corresponds to a regime where disorder is known to be relevant, that is, to change the critical exponent of the localization transition and to induce a nontrivial shift of the critical point. We show that the free energy and critical curve have an explicit universal asymptotic behavior in the weak coupling regime, depending only on the tail of the return time distribution and not on finer details of the models. This is obtained comparing the partition functions with corresponding continuum quantities, through coarse-graining techniques.