On the dimer problem and the Ising problem in finite \(3\)-dimensional lattices (Q1608298)

These two problems are expressed in terms of Pfaffians. Using Cayley's theorem that a Pfaffian can be regarded as a ``square-root'' of an antisymmetric determinant the Pfaffians are evaluated. It is claimed that this work can be extended to three-dimensional lattices such as the simple cubic lattice by introducing the concept of a generalised \(g\)-graph obtained from a finite simple cubic lattice by joining up the ``raw'' external edges.