Statistical Mechanics of Solids

It is shown that for a solid subjected to external compression or tension, statistical-mechanical calculations lead to inconsistent results unless the Hamiltonian includes terms describing the action of these external forces upon the surface atoms. This requirement is due to the existence of very long-range correlations between atoms of the solid. For liquids or gases not on the verge of a phase transition, the correlations are short ranged and the usual procedures for statistical-mechanical calculations suffice. The question of the characterization and stability of a solid is also discussed.