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Universal height fluctuations and scaling relations in interacting dimer models.

Banff International Research Station for Mathematical Innovation and Discovery

In this talk I will review the results on the universality of height fluctuations in interacting dimer models, obtained in collaboration with F. Toninelli and V. Mastropietro in a recent series of papers. The class of models of interest are close-packed dimers on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point and the dimer model with plaquette interaction. By tuning the edge weights, one can impose a non-zero average tilt for the height function, so that the considered models are in general not symmetric under discrete rotations and reflections. It is well known that, in the determinantal case, height fluctuations in the massless (or `liquid') phase scale to a Gaussian log-correlated field and their amplitude is a universal constant, independent of the tilt. Our main result is the following: when the perturbation strength is sufficiently small, log-correlations survive, with amplitude A that, generically, depends non-trivially and non-universally on the perturbation strength and on the tilt. Moreover, the amplitude A satisfies a universal scaling relation (`Haldane' or `Kadanoff' relation), saying that it equals the anomalous exponent of the dimer-dimer correlation. The proof is based on a combined use of fermionic Renormalization Group techniques, lattice Ward Identities for the lattice model and emergent Ward Identities for the infrared fixed point theory.

Mathematics; Probability Theory And Stochastic Processes

video/mp4

Author affiliation: Università degli Studi Roma Tre

2020-05-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74494

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/