Phase transitions in lattice gases with linear clusters. I. Singularities in activity and low temperature series; interacting dimers

The phase transition behavior of a lattice gas where the particles interact so as to give linear clusters is studied. High density/low temperature series show that there is an order–disorder line in the density–temperature plane. A similar model, that of interacting dimers is also studied and the temperature at which long range order sets in at close packing is estimated. Using low density activity series, the behavior of the Lee–Yang fugacity roots for these models is obtained and we conjecture on the relation of the behavior of the roots to the presence or absence of cluster surface energy.