Abstract
We consider a system of ${2}^{n}$ orientational interacting tunneling dipoles in $n$ transverse near-neighbor-well tunneling fields $^{\ensuremath{\alpha}}\ensuremath{\Delta}$ ($1>~\ensuremath{\alpha}>~n$). We show that the partition function for the system can be expressed as a product of $n$ Ising-model partition functions in transverse fields. The results are valid in one, two, and three dimensions as well as for random $\ensuremath{\Delta}$ s and random general interaction potentials.
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