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Nonanalytic Landau functionals shaping the finite-size scaling of fluctuations and response functions in and out of equilibrium

Krzysztof Ptaszyński1,2,* and Massimiliano Esposito1

  • 1Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, 30 Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg
  • 2Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland

  • *Contact author: krzysztof.ptaszynski@ifmpan.poznan.pl
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Phys. Rev. E 111, 044142 – Published 29 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.044142

Abstract

Landau theory relates phase transitions to the minimization of the Landau functional (e.g., free energy functional), which is expressed as a power series of the order parameter. It has been shown that the critical behavior of certain physical systems can be described using Landau functionals that include nonanalytic terms, corresponding to odd or even noninteger powers of the absolute value of the order parameter. In particular, these nonanalytic terms can determine the order of the phase transition and the values of the critical exponents. Here, we show that such terms can also shape the finite-size scaling behavior of fluctuations of observables (e.g., of energy or magnetization) or the response functions (e.g., heat capacity or magnetic susceptibility) at the continuous phase transition point. We demonstrate this on two examples, the equilibrium molecular zipper and the nonequilibrium version of the Curie-Weiss model.

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Phys. Rev. E 111, 044142– Published 29 April, 2025
  • Received 11 February 2025
  • Accepted 2 April 2025
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