Lattice Models of Hard-Core Molecules with Attractions: The Phase Diagram

Abstract

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 × ∞ 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.