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A gauge theory picture of an exotic transition in a dimer model

We study a phase transition in a 3D lattice gauge theory, a coarse-grained version of a classical dimer model. The dimer model on a cubic lattice, first studied by F. Alet and collaborators, displays a continuous transition between an ordered columnar phase at low temperature and a disordered phase at high temperature where dimer-dimer correlations show an algebraic decay. This is rather unusual as the standard Ginzburg-Landau theory of phase transitions generally predicts an exponential decay of correlations in the disordered phase.

This phase transition is "exotic" in the sense that it cannot be simply explained by the spontaneous symmetry breaking of an order parameter. The existence of such unconventional continuous transitions is still very controversial, numerous authors pointing at an artifact due to a very weak first-order driven process.

To have a better understanding of the dimer model, we show, using duality arguments, that the classical dimer model can be mapped to a frustrated XY spin model coupled to a gauge field. The ordering transition is then naturally understood in terms of a Higgs mechanism. A Monte-Carlo study on large system sizes of the dual model indicates a second-order transition with exponents close but slightly different from those of the simple XY model. In order to confirm the type of the transition, we perform a flowgram analysis, a powerful numerical tool to test the nature of a transition. The results of the flowgram are unambiguously pointing toward a continuous transition.

Post-scriptum :

For more details, see the original paper Gauge theory picture of an ordering transition in a dimer model, by D. Charrier, F. Alet, P. Pujol in Phys. Rev. Lett. 101, 167205 (2008)