立方均场伊辛模型的极限定理

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL Annales Henri Poincaré Pub Date : 2024-02-08 DOI:10.1007/s00023-024-01420-7

Pierluigi Contucci, Emanuele Mingione, Godwin Osabutey

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引用次数: 0

摘要

摘要我们研究了一个具有三体和二体相互作用的均场自旋模型。研究表明，大体积的平衡度量有三个纯态，即模型的三个阶段。它们包括两种磁化相反的状态和一种磁化为零的非极化状态，并在临界点合并。我们证明了中心极限定理在适当重标磁化时成立，而在临界点则出现了典型的四分行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Limit Theorems for the Cubic Mean-Field Ising Model

We study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They include the two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. We prove that the central limit theorem holds for a suitably rescaled magnetization, while its violation with the typical quartic behavior appears at the critical point.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.