2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213165We 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.7 pages, 4 figures. Minor corrections with additional figuresHigh Energy Physics - TheoryStrongly Correlated ElectronsHigh Energy Physics - LatticeMathematical PhysicsAlgebraic GeometryCombinatoricstext