THE USE OF ANTI-COMMUTING VARIABLE INTEGRALS IN STATISTICAL-MECHANICS .3. UNSOLVED MODELS

The Ising model in three dimensions is fermionized by using integrals over anticommuting variables. The result is generalized to the Ising model in arbitrary dimensions and in a magnetic field. Approximation methods are developed to attack unsolved statistical mechanics models. Perturbation theory and the Hartree approximation are applied to the unsolved monomer-dimer problems. The result is a numerical solution to this unsolved class of problems. Anticommuting variables appear to be a powerful approach to unsolved problems. © 1980 American Institute of Physics.