We consider a system of $2^n$ orientational interacting tunneling dipoles in $n$ transverse near-neighbor-well tunneling fields ${}_{}{}^{\alpha }{}_{}{}^{}\Delta$ ($1>~\alpha >~n$). 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 $\Delta$ s and random general interaction potentials.

• Received 5 May 1986

DOI:https://doi.org/10.1103/PhysRevLett.57.1355