Melting of the two-dimensional solid phase in the Gaussian core model

Abstract

A general theory for the melting of two-dimensional (2D) solids that explains the universal and nonuniversal properties remains an open problem. Although the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young theory was able to predict the critical properties of the melting transition in a variety of cases, it is already known that it could not capture the occurrence of first-order transitions observed in certain systems, nor does it provide a clear way to calculate the melting temperature for a specific model. In the present work, we have developed an analytical method that combines the self-consistent variational approximation with the renormalization group in order to deal simultaneously with the phonon fluctuations and the topological defects that are present in the melting process of 2D crystals. The method was applied with impressive success to a study of the phase diagram of the Gaussian core model, capturing not only the reentrant feature of its 2D solid phase, but also the related critical temperatures as a function of the density in quantitative detail. The developed method can be directly applied to study the melting of any hexagonal simple crystal formed by particles interacting through any finite pairwise interaction potential. Additionally, it has the potential to explain the occurrence of first-order transitions in the melting process of 2D crystals.