A Bethe model for phase transitions in the hard sphere lattice gas

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Abstract
A generalized form of the Bethe approximation is applied to the lattice gas with exclusion effects between near shells of neighbors. For short range interacting the results are in satisfactory agreement with other methods of calculation, establishing the high physical content of the approximation used. Longer ranged interactions are also considered and for the three dimensional case a new first order transition is identified. For sufficiently long ranged interactions no phase transitions are found in either two or three dimensions and reasons for this behavior are given.