Thermodynamic properties are evaluated for a onehyphen;dimensional lattice gas whose interactions satisfy the following conditions: first, arbitrary interactions, even of infinite range, are allowed within an unbroken ``queue'' of particles occupying adjacent sites; and second, the only interactions between queues are between adjacent ones, these interactions depending only on the separation of the neighboring queues. For each type of interaction a certain convergence condition is the only restriction on the form of the interaction. Two ensembles are introduced, a constant freehyphen;length ensemble and a generalized ensemble of specified intensive variables. Some examples are worked out, and it is shown generally that the model cannot lead to a firsthyphen;order phase transition.
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