Height fluctuations in non-integrable classical dimers

Abstract

We rigorously establish the asymptotic equivalence between the height function of interacting dimers on the square lattice and the massless Gaussian free field. Our theorem explains the microscopic origin of the sine-Gordon field theory description away from the free fermion point, which has previously been elusive. We use a novel technique, based on the combination of discrete holomorphicity with exact, constructive, renormalization group methods, which has the potential of being applicable to a variety of other non-integrable models at or close to criticality.

4 pages, 2 figures

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Cited by in corpus (5)

• Inhomogeneous Gaussian Free Field inside the interacting arctic curve
• Haldane relation for interacting dimers
• A Pfaffian formula for monomer-dimer partition functions
• Derivation of field theory for the classical dimer model using bosonization
• The scaling limit of boundary spin correlations in non-integrable Ising models