Dirac operator and Ising model on a compact 2D random lattice

Details Dirac operator and Ising model on a compact 2D random lattice Dirac operator and Ising model on a compact 2D random lattice

2001-10-12

arxiv.org/abs/hep-lat/0110063v1

Acta Phys.Polon. B32 (2001) 4121-4168

Physics

High Energy Physics

High Energy Physics - Lattice

Presented at the 41th Zakopane School of Theoretical Physics, 49 pages, Latex + 22 eps figures

Scientific paper

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.

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