  At low pressure, free surfaces play a crucial role in the melting transition.
Under pressure, the surface of the sample is acted upon by some pressure
transmitting medium. To examine the effect of this medium on melting, we
performed Monte Carlo simulations of a system of argon atoms in the form of a
slab with two boundaries. We examined two cases, one with a soft and the other
with a rigid medium at the boundaries. We found that in the presence of a rigid
medium, melting resembles the mechanical lattice instability found in a
surface-free solid. With a soft medium at the boundary, melting begins at the
surface and at a lower temperature. The relevance of these results to
experiment is discussed.
