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SUMMARY:Lecture 3 - The interacting dimer model  (copy) - Fabio Toninelli 
 (Université Claude Bernard Lyon 1)
DTSTART:20181012T100000Z
DTEND:20181012T113000Z
UID:TALK112108@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The aim of this minicourse is to present recent results\, obta
 ined together with Vieri Mastropietro (arXiv:1406.7710 and arXiv:1612.0127
 4)\, on non-integrable perturbations of the classical dimer model on the s
 quare lattice. In the integrable situation\, the model is free-fermionic a
 nd the large-scale fluctuations of its height function tend to a two-dimen
 sional massless Gaussian field (GFF). We prove that convergence to GFF hol
 ds also for sufficiently small non-integrable perturbations. At the same t
 ime\, we show that the dimer-dimer correlations exhibit non-trivial critic
 al exponents\, continuously depending upon the strength of the interaction
 : the model belongs\, in a suitable sense\, to the `Luttinger liquid&#39\;
  universality class. The proofs are based on constructive Renormalization 
 Group for interacting fermions in two dimensions.  &nbsp\;  Contents:  &nb
 sp\;  1. Basics: the model\, height function\, interacting dimer model. Th
 e&nbsp\;main results for the interacting model: GFF fluctuations and  &nbs
 p\;&nbsp\; Haldane relation.  &nbsp\;  2. The non-interacting dimer model:
  Kasteleyn theory\, thermodynamiclimit\, long-distance asymptotics of corr
 elations\, GFF fluctuations. Fermionic representation of the non-interacti
 ng and of the interacting dimer model.  &nbsp\;  3. Multi-scale analysis o
 f the free propagator\, Feynman diagrams and&nbsp\;dimensional estimates. 
 Determinant expansion.  &nbsp\; Non-renormalized multiscale expansion.  &n
 bsp\;  4. Renormalized multiscale expansion. Running coupling constants. B
 eta&nbsp\;function.  &nbsp\;  5. The reference continuum model (the `infra
 red fixed point&#39\;): the Luttinger model. Exact solvability of the Lutt
 inger model. Bosonization.  &nbsp\;  6. Ward identities and anomalies. Sch
 winger-Dyson equation. Closed equation for the correlation functions. Comp
 arison of the lattice&nbsp\;model with the reference one.
LOCATION:Seminar Room 2\, Newton Institute
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