On the Dimer Problem and the Ising Problem in Finite 3-dimensional Lattices

We present a new expression for the partition function of the dimer arrangements and the Ising partition function of the 3-dimensional cubic lattice. We use the Pfaffian method. The partition functions are expressed by means of expectations of determinants and Pfaffians of matrices associated with the cubic lattice.

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: Martin Loebl
• Keywords: 3-dimensional Cubic Lattice, COMBINATORICS 2002, Cubic Lattice, Partition Functions