Analyticity of a hard-core multicomponent lattice gas

A multicomponent anti-Widom-Rowlinson lattice gas is introduced. An arbitrary numberM of particle types is permitted, all having the same activity. The only interactions are nearest-neighbor exclusions oflike particles (analogous to map-coloring problems). For any lattice it is shown that there is a finite numberM ₀ (depending only on the coordination number of the lattice) such that for allMM ₀ the infinite volume correlation functions exist and are analytic functions of the activity, for all positive values of the common activity.Research supported in part by NSF Grant No. GP-33535X, AFOSR Grant No. 73-2430B, and NSF Grant No. MPS75-20638.