FM 02-15; arXiv:1502.02302

Authors: Alessandro Giuliani, Vieri Mastropietro, Fabio Toninelli

Title: Height fluctuations in non-integrable classical dimers

Sommario: We rigorously establish the asymptotic equivalence between the height function of interacting dimers on the square lattice and the massless Gaussian free eld. Our theorem explains the microscopic origin of the sine-Gordon eld 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

Alessandro Giuliani
Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, 00146 Roma Italy
giuliani@mat.uniroma3.it

Vieri Mastropietro
Dipartimento di Matematica, Università degli Studi di Milano, 20133 Milano Italy
vieri.mastropietro@unimi.it

Fabio Toninelli
CNRS and Université de Lyon, Université Lyon 1, Institut Camille Jordan, 69622 Villeurbanne France
toninelli@math.univ-lyon1.fr