Analytical solution of a one-dimensional lattice gas model with an infinite number of multiatom interactions.

We consider a one-dimensional lattice gas model in which the atoms interact via an infinite number of cluster interactions within contiguous atomic chains plus the next-nearest-neighbor pairwise interaction. All interactions are of arbitrary strength. An analytical expression for the size distribution of atomic chain lengths is obtained in the framework of the canonical ensemble formalism. Application of the exact solution to the problems of self-assembly and self-organization is briefly discussed.