Exponential decay of transverse correlations for O(N) spin systems and related models
成果类型：
Article
署名作者：
Lees, Benjamin; Taggi, Lorenzo
署名单位：
University of Bristol; University of Bristol; Sapienza University Rome
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-021-01053-5
发表日期：
2021
页码：
1099-1133
关键词：
摘要：
We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary non-zero values of the external magnetic field and arbitrary spin dimension N > 1. Our result is new when N > 3, in which case no Lee-Yang theorem is available, it is an alternative to Lee-Yang when N = 2, 3, and also holds for a wide class of multi-component spin systems with continuous symmetry. The key ingredients are a representation of the model as a system of coloured random paths, a 'colour-switch' lemma, and a sampling procedure which allows us to bound from above the 'typical' length of the open paths.
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