# Cluster expansion for the description of condensed state: crystalline cell approach

## TL;DR

This paper modifies the traditional cluster expansion to describe condensed matter by averaging over non-correlated crystal states using single-particle cell potentials, enabling better modeling of dense systems.

## Contribution

It introduces a modified cluster expansion framework based on single-particle cell potentials for describing condensed states of matter.

## Key findings

- Expansion applicable to condensed states of matter.
- Cell potentials optimized via minimum remainder condition.
- Partition function expressed through correlations of single-particle functions.

## Abstract

A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of individual clusters over the states of an ideal gas is replaced by the averaging over the states of a non-correlated crystal using single-particle cell potentials. As a result, we arrive at the expansion of the partition function in correlations on the basis of single-particle functions corresponding to the multiplicative approximation. The cell potentials defining these functions are found from the condition of the minimum of the remainder in the constructed decomposition.