Proof of the Third Law of Thermodynamics for Ising Ferromagnets

Abstract

The third law of thermodynamics is proved for a large class of Ising models with generalized ferromagnetic many-body interactions. A sufficient condition for the third law to hold is that the model have nearest-neighbor couplings which are bounded from below by a positive constant. The proof is based on a spin-correlation inequality of Griffiths which implies a corresponding inequality for the bulk entropy per spin. Ground-state degeneracy considerations are completely avoided.