Free energy analysis for a system of interacting particles arranged in Bravais lattice

TL;DR

This paper introduces a method for calculating free energy in lattice systems with interactions, addressing divergences in infinite systems, and applies it to dusty plasma grains and electrons on liquid helium.

Contribution

It presents a novel approach to free energy calculation for interacting particle systems in Bravais lattices, handling divergences and extending to quantum cases.

Findings

Calculated lattice parameters for dusty plasma grains.

Determined localization distance for electrons on liquid helium.

Identified conditions for electron lattice formation.

Abstract

We propose a method of free energy calculation for a system of interacting particles arranged in a Bravais lattice. It will be shown how to treat divergences for infinite unbounded systems with "catastrophic" potetntials like Coulomb and compare two of them. Besides, we show that current method may be used not only for essentially classical systems, but for some quantum as well. Two systems are considered: grains in dusty plasma and electrons on the liquid-helium surface. For dusty-plasma parameters of grain's lattice are calculated by numerical solution of obtained equations. Electrons on the liquid-helium surface are analyzed to get localization distance. Besides, conditions for existence of electron lattice are found.