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

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.