Geodesic
On the dimer problem and the Ising problem in finite \(3\)-dimensional lattices
The electronic journal of combinatorics, Tome 9 (2002)
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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.
DOI : 10.37236/1646
Classification : 05C90, 82B20, 82B41
Mots-clés : Pfaffian 
@article{10_37236_1646,
     author = {Martin Loebl},
     title = {On the dimer problem and the {Ising} problem in finite \(3\)-dimensional lattices},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1646},
     zbl = {1024.05084},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1646/}
}
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%A Martin Loebl
%T On the dimer problem and the Ising problem in finite \(3\)-dimensional lattices
%J The electronic journal of combinatorics
%D 2002
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Martin Loebl. On the dimer problem and the Ising problem in finite \(3\)-dimensional lattices. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1646

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