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

TL;DR

This paper explores how nonanalytic terms in Landau functionals influence the finite-size scaling of fluctuations and response functions at phase transitions, with applications to both equilibrium and nonequilibrium models.

Contribution

It demonstrates that nonanalytic terms in Landau functionals shape finite-size scaling behavior of fluctuations and responses in phase transitions, extending traditional Landau theory.

Findings

Nonanalytic Landau functionals affect finite-size scaling of fluctuations.

Application to equilibrium molecular zipper model.

Application to nonequilibrium Curie--Weiss model.

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.