Volume 109, Number 6, March 2015
|Number of page(s)||5|
|Published online||25 May 2015|
Height fluctuations in non-integrable classical dimers
1 Dipartimento di Matematica e Fisica, Università di Roma Tre - L.go S. L. Murialdo 1, 00146 Roma, Italy
2 Dipartimento di Matematica, Università degli Studi di Milano - Via Saldini, 50, 20133 Milano, Italy
3 CNRS and Université de Lyon, Université Lyon 1, Institut Camille Jordan - 43 bd du 11 novembre 1918, 69622 Villeurbanne, France
Received: 20 February 2015
Accepted: 20 March 2015
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.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.) / 64.60.F- – Equilibrium properties near critical points, critical exponents
© EPLA, 2015
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