  We construct a mean field theory for the lattice model of a structural glass
and solve it using the replica method and one step replica symmetry breaking
ansatz; this theory becomes exact in the limit of infinite dimensions.
Analyzing stability of this solution we conclude that the metastable states
remain uncorrelated in a finite temperature range below the transition, but
become correlated at sufficiently low temperature. We find dynamic and
thermodynamic transition temperatures as functions of the density and construct
a full thermodynamic description of a typical physical process in which the
system gets trapped in one metastable state when cooled below vitrification
temperature. We find that for such physical process the entropy and pressure at
the glass transition are continuous across the transition while their
temperature derivatives have jumps.
