Power-law correction in the probability density function of the critical Ising magnetization

IF 1.1 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-06 DOI:10.1007/s11040-025-09517-z

Federico Camia, Omar El Dakkak, Giovanni Peccati

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引用次数: 0

Abstract

At the critical point, the probability density function of the Ising magnetization is believed to decay like \(\exp {(-x^{\delta +1})}\), where \(\delta \) is the Ising critical exponent that controls the decay to zero of the magnetization in a vanishing external field. In this paper, we discuss the presence of a power-law correction \(x^{\frac{\delta -1}{2}}\), which has been debated in the physics literature. We argue that whether such a correction is present or not is related to the asymptotic behavior of a function that measures the extent to which the average magnetization of a finite system with an external field is influenced by the boundary conditions. Our discussion is informed by a mixture of heuristic calculations and rigorous results. Along the way, we review some recent results on the critical Ising model and prove properties of the average magnetization in two dimensions which are of independent interest.

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临界伊辛磁化的概率密度函数的幂律修正

在临界点处，伊辛磁化的概率密度函数被认为像\(\exp {(-x^{\delta +1})}\)一样衰减，其中\(\delta \)是控制在消失的外场中磁化衰减到零的伊辛临界指数。在本文中，我们讨论了幂律修正\(x^{\frac{\delta -1}{2}}\)的存在，这在物理文献中一直存在争议。我们认为，是否存在这样的修正与一个函数的渐近行为有关，该函数测量具有外场的有限系统的平均磁化程度受边界条件的影响。我们的讨论是由启发式计算和严格的结果混合而成的。在此过程中，我们回顾了一些关于临界伊辛模型的最新结果，并证明了二维平均磁化的性质，这是一个独立的兴趣。

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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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.