Does the method of quasi-averages lead to the periodic density in a crystal?

TL;DR

The paper critically examines the method of quasi-averages, demonstrating it does not produce the periodic density characteristic of crystals, and discusses alternative approaches to studying crystalline states via statistical mechanics.

Contribution

It shows that the method of quasi-averages fails to generate periodic density in crystals, challenging its traditional use for modeling crystalline states.

Findings

Quasi-averages do not lead to periodic density in crystals.

Gibbs distribution remains spatially uniform.

Alternative methods are needed to study crystalline states.

Abstract

Since the Gibbs distribution function always yields a density of particles constant in space, in order to obtain the periodic density characteristic of a crystal it is usual to mention the method of quasi-averages. In the present paper it is shown that the method of quasi-averages does not lead to the periodic density as well as the initial Gibbs distribution. It is also discussed how the crystalline state can be investigated by means of statistical mechanics.