Abstract
We study the validity of the third law of thermodynamics and the occurrence of a nonzero residual entropy in discrete spin systems. For a general classical spin system on a d-dimensional hypercubic lattice with isotropic, translationally invariant, nearest-neighbor interactions, we establish the following. (i) The necessary and sufficient condition for the third law to hold. (ii) A lower bound on the residual entropy when the third law is not valid. It is also established that the residual entropy is nonzero for all d, if it is nonzero in any dimension d>1. .AE
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