Abstract: In these lectures I will give an introduction to the methods of fermionic Renormalization Group and multiscale analysis for some 2-dimensional, non-exactly solvable statistical mechanics models, focusing on the case of close-packed interacting dimer models. I will first define the weakly interacting dimer model and review recent results (in collaboration with V. Mastropietro and F. Toninelli) on the GFF behavior of the height function. Next I will explain how to compute ther-modynamic functions via convergent fermionic perturbation theory, focusing on the free energy. After having explained why naive perturbation theory fails, I will describe renormalized multi-scale expansion and prove its convergence, under the assumption that the effective, scale-dependent, interaction strength remains small, uniformly in the scale index. Finally, I will explain the origin of the cancellations leading to the proof of boundedness of the effective interaction strength, which can be traced back to the exact solvability of a reference model (similar to the Luttinger model) whose asymptotic large-distance behavior is the same as the interacting dimer model.

Schedule:
12.12.2022 – 14:00 - 16:00
13.12.2022 – 14:00 - 16:00
15.12.2022 – 10:00 - 12:00
16.12.2022 – 10:00 - 12:00

Venue: TU Wien, Freihaus Building, Seminarraum DB Gelb 04
Wiedner Hauptstrasse 10, A-1040 Wien, Austria

Contact: fabio.toninelli @ tuwien.ac.at