对旋 SK 模型在两个尺度上的自由能波动

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields Pub Date : 2024-07-02 DOI:10.1007/s00440-024-01296-y

Anton Bovier, Adrien Schertzer

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引用次数: 0

摘要

20 年前，Bovier、Kurkova 和 Löwe （Ann Probab 30(2):605-651, 2002）证明了高温下自旋玻璃的 Sherrington-Kirkpatrick 模型 p 自旋版本中自由能波动的中心极限定理（CLT）。在本文中，我们从两个方面改进了他们的结果。首先，我们扩展了温度范围，以涵盖已知淬火和退火自由能重合的整个体系。其次，我们将波动的主要来源确定为一个纯粹的耦合相关项，并进一步展示了围绕这一随机对象的自由能偏差的 CLT。

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Fluctuations of the free energy in p-spin SK models on two scales

20 years ago, Bovier, Kurkova, and Löwe (Ann Probab 30(2):605–651, 2002) proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington–Kirkpatrick model of spin glasses at high temperatures. In this paper we improve their results in two ways. First, we extend the range of temperatures to cover the entire regime where the quenched and annealed free energies are known to coincide. Second, we identify the main source of the fluctuations as a purely coupling dependent term, and we show a further CLT for the deviation of the free energy around this random object.

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来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.