Topological Phase Transitions and Holonomies in the Dimer Model

Nash, Charles and O'Connor, Denjoe (2008) Topological Phase Transitions and Holonomies in the Dimer Model. (Preprint)

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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 modular parameter of the torus goes to zero 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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 13:47
Last Modified: 14 Dec 2022 14:46

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