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

Martin Loebl

Abstract


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.


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