Topological Phase Transitions and Holonomies in the Dimer Model

Details Topological Phase Transitions and Holonomies in the Dimer Model Topological Phase Transitions and Holonomies in the Dimer Model

2008-09-17

arxiv.org/abs/0809.2960v3

J.Phys.A42:012002,2009

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, 4 figures. Minor corrections with additional figures

Scientific paper

10.1088/1751-8113/42/1/012002

We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite size corrections to the bulk partition function correspond to a massless Dirac Fermion in the presence of a flat connection with nontrivial holonomy. For general bond activities we find that the phase transition in this model is a topological one, where the torus degenerates and its modular parameter becomes real at the critical temperature. We argue that these features are generic to bipartite dimer models and we present a more general lattice whose continuum partition function is that of a massive Dirac Fermion.

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