Article révisé par les pairs
|Two different lattice models of hard-core molecules with attractions are discussed. Both of them refer to a square lattice, and the excluded range around a molecule covers first-, second-, and third-neighboring sites. For Model I the attractive range corresponds to fifth neighbors only; for Model II it includes fourth neighbors as well as fifth neighbors, with a slightly more pronounced attraction on fourth neighbors. The exact properties of finite lattices 10 X °> are investigated by the matrix method for both models, and it is shown that they exhibit (at least) two phase transitions in some temperature range. These transitions are apparently first-order ones and seem to correspond to the gas-liquid and fluid-solid phase changes. Model I leads to a rather unphysical phase diagram similar to that of helium. On the other hand, Model II gives a phase diagram essentially similar to the one observed for simple classical substances.