Combinatorial and topological approach to the 3D Ising model

Details Combinatorial and topological approach to the 3D Ising model Combinatorial and topological approach to the 3D Ising model

1999-09-13

arxiv.org/abs/cond-mat/9909168v2

J.Phys.A33:741-761,2000

Physics

Condensed Matter

Statistical Mechanics

33 pages, 5 figures

Scientific paper

10.1088/0305-4470/33/4/308

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.

Affiliated with

Also associated with

No associations

Rating

Combinatorial and topological approach to the 3D Ising model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Combinatorial and topological approach to the 3D Ising model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Combinatorial and topological approach to the 3D Ising model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-464328