Long range order for three-dimensional random field Ising model throughout the entire low temperature regime

IF 2.6 1区 数学 Q1 MATHEMATICS Inventiones mathematicae Pub Date : 2024-07-31 DOI:10.1007/s00222-024-01283-z
Jian Ding, Yu Liu, Aoteng Xia
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Abstract

For \(d\geq 3\), we study the Ising model on \(\mathbb{Z}^{d}\) with random field given by \(\{\epsilon h_{v}: v\in \mathbb{Z}^{d}\}\) where \(h_{v}\)’s are independent normal variables with mean 0 and variance 1. We show that for any \(T < T_{c}\) (here \(T_{c}\) is the critical temperature without disorder), long range order exists as long as \(\epsilon \) is sufficiently small depending on \(T\). Our work extends previous results of Imbrie (1985) and Bricmont–Kupiainen (1988) from the very low temperature regime to the entire low temperature regime.

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三维随机场伊辛模型在整个低温体系中的长程有序性
对于(d\geq 3\), 我们研究的是\(\mathbb{Z}^{d}\)上的伊辛模型,其随机场由\(\{epsilon h_{v}: v\in \mathbb{Z}^{d}\)给出,其中\(h_{v}\)是均值为0、方差为1的独立正态变量。我们证明,对于任意 \(T < T_{c}\) (这里 \(T_{c}\) 是无序的临界温度),只要 \(\epsilon \) 足够小,就会存在长程有序性。我们的研究将 Imbrie(1985)和 Bricmont-Kupiainen(1988)之前的研究成果从超低温体系扩展到了整个低温体系。
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来源期刊
Inventiones mathematicae
Inventiones mathematicae 数学-数学
CiteScore
5.60
自引率
3.20%
发文量
76
审稿时长
12 months
期刊介绍: This journal is published at frequent intervals to bring out new contributions to mathematics. It is a policy of the journal to publish papers within four months of acceptance. Once a paper is accepted it goes immediately into production and no changes can be made by the author(s).
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