REASONABLE AND ROBUST HAMILTONIANS VIOLATING THE 3RD LAW OF THERMODYNAMICS

It has recently been shown that the third law of thermodynamics is vio lated by an entire class of classical Hamiltonians in one dimension, o ver a finite volume of coupling-constant space, assuming only that cer tain elementary symmetries are exact, and that the interactions are fi nite ranged. However, until now, only the existence of such Hamiltonia ns was known, while almost nothing was known of the nature of the coup lings. Here we show how to define the subvolume of these Hamiltonians- a ''wedge'' W in a d-dimensional space-in terms of simple properties o f a directed graph. We then give a simple expression for a specific Ha miltonian H in this wedge, and show that H* is a physically reasonabl e Hamiltonian, in the sense that its coupling constants lie within an envelope that decreases smoothly, as a function of the range I, to zer o at l= r+1, where r is the range of the interaction.