Two different lattice models of hardhyphen;core molecules with attractions are discussed. Both of them refer to a square lattice, and the excluded range around a molecule covers firsthyphen;, secondhyphen;, and thirdhyphen;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 10thinsp;times;thinsp;infin; 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 firsthyphen;order ones and seem to correspond to the gasndash;liquid and fluidndash;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.
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