Dirac operator and Ising model on a compact 2D random lattice
High Energy Physics - Lattice
2007-05-23 v1
Abstract
Lattice formulation of a fermionic field theory defined on a randomly triangulated compact manifold is discussed, with emphasis on the topological problem of defining spin structures on the manifold. An explicit construction is presented for the two-dimensional case and its relation with the Ising model is discussed. Furthermore, an exact realization of the Kramers-Wannier duality for the two-dimensional Ising model on the manifold is considered. The global properties of the field are discussed. The importance of the GSO projection is stressed. This projection has to be performed for the duality to hold.
Cite
@article{arxiv.hep-lat/0110063,
title = {Dirac operator and Ising model on a compact 2D random lattice},
author = {L. Bogacz and Z. Burda and J. Jurkiewicz and A. Krzywicki and C. Petersen and B. Petersson},
journal= {arXiv preprint arXiv:hep-lat/0110063},
year = {2007}
}
Comments
Presented at the 41th Zakopane School of Theoretical Physics, 49 pages, Latex + 22 eps figures