Combinatorial and topological approach to the 3D Ising model
| dc.creator | Regge, Tullio | |
| dc.creator | Zecchina, Riccardo | |
| dc.date | 1999-09-13 | |
| dc.date | 1999-09-23 | |
| dc.date.accessioned | 2026-07-07T11:34:17Z | |
| dc.date.available | 2026-07-07T11:34:17Z | |
| dc.description | We extend the planar Pfaffian formalism for the evaluation of the Ising partition function to lattices of high topological genus g. The 3D Ising model on a cubic lattice, where g is proportional to the number of sites, is discussed in detail. The expansion of the partition function is given in terms of 2^{2 g} Pfaffians classified by the oriented homology cycles of the lattice, i.e. by its spin-structures. Correct counting is guaranteed by a signature term which depends on the topological intersection of the oriented cycles through a simple bilinear formula. The role of a gauge symmetry arising in the above expansion is discussed. The same formalism can be applied to the counting problem of perfect matchings over general lattices and provides a determinant expansion of the permanent of 0-1 matrices. | |
| dc.description | 33 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9909168 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9909168 | |
| dc.identifier | J.Phys.A33:741-761,2000 | |
| dc.identifier | doi:10.1088/0305-4470/33/4/308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/198192 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Combinatorics | |
| dc.title | Combinatorial and topological approach to the 3D Ising model | |
| dc.type | text |