• Open Access

Lee-Yang theory of the Curie-Weiss model and its rare fluctuations

Aydin Deger and Christian Flindt
Phys. Rev. Research 2, 033009 – Published 2 July 2020

Abstract

Phase transitions are typically accompanied by nonanalytic behaviors of the free energy, which can be explained by considering the zeros of the partition function in the complex plane of the control parameter and their approach to the critical value on the real axis as the system size is increased. Recent experiments have shown that partition function zeros are not just a theoretical concept. They can also be determined experimentally by measuring fluctuations of thermodynamic observables in systems of finite size. Motivated by this progress, we investigate here the partition function zeros for the Curie-Weiss model of spontaneous magnetization using our recently established cumulant method. Specifically, we extract the leading Fisher and Lee-Yang zeros of the Curie-Weiss model from the fluctuations of the energy and the magnetization in systems of finite size. We develop a finite-size scaling analysis of the partition function zeros, which is valid for mean-field models and which allows us to extract both the critical values of the control parameters and the critical exponents, even for small systems that are away from criticality. We also show that the Lee-Yang zeros carry important information about the rare magnetic fluctuations as they allow us to predict many essential features of the large-deviation statistics of the magnetization. This finding may constitute a profound connection between Lee-Yang theory and large-deviation statistics.

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  • Received 13 February 2020
  • Revised 7 April 2020
  • Accepted 17 June 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033009

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Aydin Deger and Christian Flindt

  • Department of Applied Physics, Aalto University, 00076 Aalto, Finland

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Issue

Vol. 2, Iss. 3 — July - September 2020

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