  The understanding of thermodynamic glass transition has been hindered by the
lack of proper models beyond mean-field theories. Here, we propose a
three-dimensional lattice glass model on a simple cubic lattice that exhibits
the typical dynamics observed in fragile supercooled liquids such as two-step
relaxation, super-Arrhenius growth in the relaxation time, and dynamical
heterogeneity. Using advanced Monte Carlo methods, we compute the thermodynamic
properties deep inside the glassy temperature regime, well below the onset
temperature of the slow dynamics. The specific heat has a finite jump towards
the thermodynamic limit with critical exponents close to those expected from
the hyperscaling and the random first-order transition theory for the glass
transition. We also study an effective free energy of glasses, the
Franz--Parisi potential, as a function of the overlap between equilibrium and
quenched configurations. The effective free energy indicates the existence of a
first-order phase transition, consistent with the random first-order transition
theory. These findings strongly suggest that the glassy dynamics of the model
has its origin in thermodynamics.
