Journal of Statistical Physics, Vol. 24, No. 1, 1981, p. 279-297.
The third law of thermodynamics, in the sense that the entropy per unit volume
goes to zero as the temperature goes to zero, is investigated within the frame-
work of statistical mechanics for quantum and classical lattice models. We
present two main results: (i) For all models the question of whether the third law
is satisfied can be decided completely in terms of ground-state degeneracies
alone, provided these are computed for all possible "boundary conditions." In
principle, there is no need to investigate possible entropy contributions from
low-lying excited states. (ii) The third law is shown to hold for ferromagnetic
models by an analysis of the ground states.