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We consider a 1D lattice gas model in which the atoms interact via aninfinite number of cluster interactions within contiguous atomic chains plusthe next nearest neighbor pairwise interaction. All interactions are ofarbitrary strength. An analytical expression for the size distribution ofatomic chain lengths is obtained in the framework of the canonical ensembleformalism. Application of the exact solution to the problems of self-assemblyand self-organization is briefly discussed.Comment: 12 pages, 3 figure

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