Topological Phase Transitions and Holonomies in the Dimer Model
Nash, Charles and O'Connor, Denjoe (2009) Topological Phase Transitions and Holonomies in the Dimer Model. Journal of Physics A: Mathematical and Theoretical, 42 (1). pp. 1-8. ISSN 1751-8121
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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