Structural glass on a lattice in the limit of infinite dimensions

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.