Work

Generalization of the central limit theorem to critical systems: Revisiting perturbation theory

Year: 2025

Type: article

Abstract: The central limit theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization mode has been performed with the functional renormalization group in the case of the three-dimensional Ising model [Balog et al., Phys. Rev. Lett. 129, 210602 (2022)10.1103/PhysRevLett.129.210602]. It has been shown in that article that there exists an entire family of universal PDFs parameterized by ζ=lim_{L,ξ_{∞}→∞}L/ξ_{∞} which is the ratio of the system size L to the bulk correlation length ξ_{∞} with both the thermodynamic limit and the critical limit being taken simultaneously. We show how these PDFs or, equivalently, the rate functions which are their logarithm, can be systematically computed perturbatively in the ε=4-d expansion. We determine the whole family of universal PDFs and show that they are in good qualitative agreement with Monte Carlo data. Finally, we conjecture on how to significantly improve the quantitative agreement between the one-loop and the numerical results.

Source: Physical review. E

DOI: 10.1103/physreve.111.034128

Authors: Sankarshan Sahu, Bertrand Delamotte, Adam Rançon

Institutions: Sorbonne Université, Laboratoire de Physique Théorique de la Matière Condensée, Université de Lille, Laboratoire de Physique des Lasers, Atomes et Molécules

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green