A general theory of two-dimensional melting: the Gaussian-core model explained

A general theory for the melting of two dimensional solids explaining the variety of scenarios observed in different kind of models is up to date an open problem. Although the celebrated KTHNY theory have been able to predict the critical properties of the melting transition in a variety cases, it is already known that it is not able to capture the occurrence of first order transitions observed in certain systems. Moreover the analytical determination of non-universal quantities like the melting temperature within this theory remains widely open. In the present work we have developed a method that combines Self Consistent Variational Approximation with the Renormalization Group in order to deal simultaneously with the phonon fluctuations and the topological defects present in the melting process of two dimensional crystals. The method was applied with impressive success to the 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 two dimensional crystals