"Coulombic" transitions in three-dimensional dimer models
A common challenge in complex materials is the presence of interactions that act on multiple energy scales. In some cases, the strongest interactions can be regarded as imposing constraints on the accessible phase space. When the temperature is low compared to these strong interactions, the system fluctuates and/or orders within the constrained space. It has recently been recognized that in some cases, such constraints can give rise to remarkable emergent phenomena, even in the classical limit. This may occur in some frustrated magnets [see e.g. 1 or 2 or 3 ], or perhaps even in water ice! One can observe unusual correlations in a nominally disordered phase, and unconventional criticality in phase transitions, violating the venerable Landau paradigm.
A convenient theoretical testbed for this phenomena is provided by classical dimer models, which by their definition embody a local constraint. Recent simulations of such models have indeed observed unconventional criticality [see 4 ]. But the systematics and underlying field theory of this criticality remains controversial.
^ TOPOur work:
We combined extensive Monte Carlo simulations of a large family of dimer models, with a phenomenological field theory derived using the ideas originally formulated in Ref.[ 1 ], to explore this phenomena in much more generality than previously attempted. We find that the field theory, which is a sort of Coulomb gauge theory (multi-component Ginzburg-Landau), correctly predicts the systematic behaviors for the entire family of models. We take this as strong evidence that we have identified correctly the continuum field theory description of these dimer models.
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