Equilibrium fluctuations in a metastable state of a Ginzburg-Landau system

TL;DR

This paper investigates the thermal fluctuation properties of a metastable phase in a Ginzburg-Landau system, combining theoretical perturbation analysis with numerical simulations to understand phase coexistence and fluctuations.

Contribution

It provides a combined theoretical and numerical analysis of fluctuation properties in an asymmetric, athermal Ginzburg-Landau system, highlighting differences from symmetric thermal cases.

Findings

Numerical results agree with theoretical predictions within numerical accuracy.

Discrepancies found in the dependence of internal energy on supersaturation.

Results aid in modeling nucleation and rare events in Ginzburg-Landau systems.

Abstract

We calculate thermal fluctuation properties: volume-averaged order parameter, Helmholtz free and internal energies, and their variances of a supersaturated disordered phase in the Gibbs canonical ensemble for an asymmetric (third-order interactions), athermal (independence of the supersaturation and thermal noise) effective Hamiltonian. These properties are different from those of the symmetric thermal one with the most important differences being the phase coexistence and "thermal expansion." The fluctuation properties of the system were calculated theoretically, using the perturbation method, and numerically, using the "brute force" simulations method. Overall, the numerical calculations match the theory within the accuracy of the numerical method. However, a discrepancy of the dependence of the internal energy and its variance on the supersaturation exists. Results of the present study can be used for calculations of the fluctuation properties of the systems and modeling of nucleation and other rare events in the framework of the Ginzburg-Landau method.