Analytical solution of 1D lattice gas model with infinite number of multiatom interactions

TL;DR

This paper derives an exact analytical solution for a one-dimensional lattice gas model with infinite multi-atom interactions and next-nearest neighbor interactions, providing insights into atomic chain size distributions and self-assembly processes.

Contribution

It presents the first exact analytical expression for chain length distribution in a 1D lattice gas with infinite cluster interactions and next-nearest neighbor effects.

Findings

Derived an explicit formula for chain size distribution.

Applicable to self-assembly and self-organization phenomena.

Provides a framework for analyzing complex atomic interactions.

Abstract

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.