Analytical solution of 1D lattice gas model with infinite number of   multiatom interactions
  We consider a 1D 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. 
V. I. Tokar and H. Dreyss\'e