A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

TL;DR

This paper presents a new method based on classical nucleation theory to accurately estimate the critical nucleus size and surface tension in first-order phase transition systems, effective even with small system sizes.

Contribution

The novel approach allows calculation of critical nucleus and surface tension without requiring an infinite volume limit, unlike previous methods.

Findings

Method successfully tested on two 2D lattice systems

Provides reliable estimates with small system sizes

Cannot be applied at the critical point or near coexistence

Abstract

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.