The first microscopic theory of surface melting have been developed by A. Troyanov and E. Tossati . For a microscopic theory, one would need for a start a simple and accurate model, capable of accounting for the bulk phase diagram including solid, liquid and vapor phases, the triple point and the critical point of any substance. Such a complete theory has not yet been developed and the very basic building block for a microscopic surface melting theory is missing.
Nevertheless A. Troyanov and E. Tossati  developed a theory of surface melting, based on the fact that at the price of introducing a discrete reference lattice and using a drastic simplification like the mean-field approach, the partition function, , of a system of particles interacting via a pairwise potential can be calculated. In order to calculate the free energy of an assembly of atoms they introduced a reference lattice. The volume of each cell is chosen to be so small, that possibility of multiple occupancy of a lattice cell can be neglected.
The partition function is:
In order to describe order-disorder transition two order
parameters - ``crystallinity'', , and average density, , are defined and
calculated for each layer of the reference lattice separately.
The ``crystallinity'' in each layer is given by:
According to the calculation, surface melting takes place both on the (100) and (110) surfaces. A thin liquid-like film gradually appears at the surface region. The crystallinity inside the quasiliquid film drops rapidly to zero, and also density is jumping rather abruptly from liquid-like to solid-like (See Fig.), but this drastic change of the density is seem to be due to the mean-field approximation, e.g. due to ignoring of fluctuations. Molecular dynamics studies have shown substantially broader transition from a solid-like to liquid-like region in surface premelting.
In order to understand the influence of the form of the inter-atomic potential on surface melting A. Troyanov and E. Tossati  investigated the phenomenon when the sign of the tail of the LJ potential was reversed. The physical origin of such a weak repulsive at long-range distance was not proposed and the reversion was merely considered as a tool for better understanding of the phenomenon. But it seems plausible, that many-body interactions might effectively lead to a long-range repulsion.
It turns out that a small change of the interatomic potential has a dramatic effect on surface melting. The surface starts to melt, i.e. few layers become disordered with the increase of temperature, but further increase of temperature does not increase the number of molten layers. This phenomenon is called ``blocked surface melting'' (an analog of incomplete wetting). This ``blocked surface melting'' was predicted by phenomenological theories of surface melting  and also was observed experimentally at the Ge(111) surface . It was concluded that the mode of growth of the quasiliquid layer is extremely fragile and sensitive to the range and sign of the interatomic potential.
This theory excludes fluctuations, which may play an important rôle in surface melting. For example, both the solid-liquid and the liquid-vapor interfaces are expected to execute very close to a joint ``meandering'', i.e. out-of-plane fluctuations, which is typical for all surfaces about their roughening temperature. It is not clear that effect could roughening have on the results predicted by the model. Surface melting and roughening are, respectively, short-range and long-range phenomena, and need not necessarily interfere one with another. It may happen that locally, on a short-range scale, the physics is described by surface melting, while globally only roughening will matter, irrespective of whether surface melting taking place or not. If in-plane fluctuations are considered, then there is a possibility of a ``first layer melting''  at temperatures of order . This transition is acting as a kind of ``gateway'' to the subsequent development of a quasiliquid layer. The surface layers become shear unstable due to anharmonic effects and diffusion of the surface atoms sets in.