Magnetic model for supersolidity

The well known correspondence between the lattice liquid (or solid) model and a magnetic model like the Ising model, is used to obtain the thermodynamic properties of an one-dimensional quantum crystal whose lattice is divided in two different interpenetrating sublattices α and β. Among others, we introduce a Bose-Einstein condensation and an order-disorder parameters to solve the equilibrium state. Then, we calculate the Helmholtz free energy in a mean field theory approximation and, applying the standard minimization method respect to the condensate and order-disorder parameters, we find a critical temperature different from zero at which the system presents a phase transition like the Bose-Einstein condensation which we connect with the possibility of a supersolid transition.