Factorial Moments in a Generalized Lattice Gas Model

We construct a simple multicomponent lattice gas model in one dimension in which each site can either be empty or occupied by at most one particle of any one of $D$ species. Particles interact with a nearest neighbor interaction which depends on the species involved. This model is capable of reproducing the relations between factorial moments observed in high--energy scattering experiments for moderate values of $D$. The factorial moments of the negative binomial distribution can be obtained exactly in the limit as $D$ becomes large, and two suitable prescriptions involving randomly drawn nearest neighbor interactions are given. These results indicate the need for considerable care in any attempt to extract information regarding possible critical phenomena from empirical factorial moments.