  A general theory for the melting of two dimensional solids explaining the
universal and non-universal properties is an open problem up to date. 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 as well as it doesn't 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 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.
