Square lattice hard-core bosons within the random phase approximation

Using random phase approximation we build finite-temperature phase diagrams and calculate thermodynamic functions of a square lattice hard-core boson model with nearest (nn) and next-nearest-neighbor (nnn) interactions in terms of equivalent to it an anisotropic spin-1/2 XXZ model in a magnetic field. The system undergoes liquid-solid phase transitions that can be either of the first or second order. Depending on the hopping value and ratio between nn and nnn interactions the system displays two types of critical behavior. The line of the first-order transitions terminates in a bicritical end point inside the solid phase or ends in a tricritical point continuously giving way to the second-order phase transition line. The connection of the hopping and the ratio between the nn and nnn interactions with criticality of the system is investigated. The critical line separating the regions of specific critical behavior is built. Reentrant liquid-solid-liquid phase transitions are found and discussed.