Extent of exponent variation in a hard-square lattice gas with second-neighbor repulsion

The critical exponents of a class of transitions observable in adsorbed systems have been predicted to be nonuniversal. The extent of this variation for physical systems is of obvious experimental interest. We calculate this extent in a model which exhibits such a transition and which may be appropriate to physisorption on square substrates, a lattice gas with nearest-neighbor exclusion and second-neighbor repulsion. We apply phenomenological scaling methods to strips of finite width and find an ordered phase near density {} characterized by a thermal exponent yT which varies with density from 0.9 to at least 1.5. For completeness, the case of a second-neighbor attraction is also considered. The expected universality of the resultant transition is obtained and its tricritical point located.