Abstract
The pyrochlore lattice is a three-dimensional (d=3) periodic array of corner-sharing regular tetrahedra. An Ising model is defined upon this lattice as having a 4-spin “volume” interaction among the corner Ising spins of each elementary tetrahedron. The model is solved exactly and shown to be devoid of any finite-temperature phase transition, thereby remaining in a disordered (high-temperature) phase. Exact solutions are found for all multisite correlations which are then used to obtain exact solutions for specific heat, initial and non-linear parallel magnetic susceptibilities as well as initial perpendicular susceptibility, inelastic neutron scattering function, and the joint configurational probabilities of the Ising spins. All solutions are simple algebraic functions of K and tanh K (K being the multispin coupling parameter) and exhibit such behaviors as rounded extrema, crossing points, sigmoidal curves having non-vertical inflection points, and the like. Despite their “analytical quiescence”, most of these simple solutions are evidently the first exact explicit expressions for the selected physical quantities to appear in the literature for classical and quantal d=3 Ising models having multispin “volume” interactions, with the prospect of offering some guidance and insights upon a larger class of multisite-interaction model systems.
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