Statistical Mechanics: Recent Results

Workshop at IME-USP

12 July 2021 - (9h a.m. - 1h p.m.) - São Paulo - (GMT-3)

Workshop with experts and young researchers in statistical mechanics, in particular, talks about recent results on Ising-type models.

VIDEO OF THE WORKSHOP

São Paulo - (9h a.m. - 1h p.m.) - Roma - (2h p.m. - 6h p.m.) - Gèneve - (2h p.m. - 6h p.m.) - Victoria (British Columbia) - (5h a.m. - 9h a.m.)


Speakers:


Titles and Abstracts

(9h-10h) Speaker: Alessandro Giuliani (Università degli Studi Roma Tre & Centro Linceo Interdisciplinare B. Segre)

Title: Scaling limit and finite-size corrections of 2D non-planar Ising models. (SLIDES) (VIDEO)

Abstract: In the last few years, the methods of constructive fermionic Renormalization Group (RG) have successfully been applied to the study of the scaling limit of several 2D statistical mechanics models at the critical point, including the 2D Ising with finite range interactions. Different instances of universality have been proved in this context, including the fact that the scaling limit of the energy-energy correlations in cylindrical geometry and the central charge (computed from the leading sub-leading contribution to the critical free energy on the torus) are independent of the interaction. Compared to previous constructive RG methods, our techniques are capable of computing the critical thermodynamic observables at a precision that goes beyond the leading order in the system size, and may be relevant for the study of the flow of the effective boundary conditions and the computation of boundary critical exponents in more general critical models in finite domains. Based on joint works with R. Greenblatt, V. Mastropietro and G. Antinucci.

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(10h-11h) Speaker: Sébastien Ott (Université de Genève)

Title: Interfaces in the Ising model and their SOS limit: old and new. (SLIDES) (VIDEO)

Abstract: A fundamental problem of statistical physics is the description of phase coexistence. It involves, in particular, the study of interfaces separating two stable phases. A classical model in which one can investigate this problem is the Ising model on Z^d with Dobrushin boundary conditions below the critical temperature.

After a short introduction on the Ising model and its Solid-On-Solid limit, I will review existing results on the large-scale behaviour of interfaces at low temperature. In dimension 2, a rather complete picture is available with proven invariance principles in various geometries both for the Ising model and its 1 dimensional SOS limit. In higher dimensions, the picture is less complete and I will discuss available results for the SOS model and conjectures for the Ising model. The main open problem for the Ising model is the existence of a roughening transition in dimension 3. While the question is still out of reach for the Ising model, results are available in its 2 dimensional SOS limit since the 1981 groundbreaking paper of Fröhlich and Spencer on the BKT transition. If time permits, I will conclude by sketching a new 'soft' proof of the roughening transition for the SOS model in dimension 2.

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(11h-12h) Speaker: Lucas Affonso (University of São Paulo (USP), Brazil/University of Victoria (Uvic), Canada)

Title: Fröhlich-Spencer revisited: a contour argument for long-range Ising models (SLIDES) (VIDEO)

Abstract: Inspired by Fröhlich-Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a contour analysis and a direct proof for the phase transition for ferromagnetic long-range Ising models on the multidimensional integer lattice. We start this talk by addressing the difference between our contours and the ones appearing in previous papers. As an application, we prove the persistence of the phase transition when we add a polynomial decaying magnetic field.

The talk is based on joint work with Rodrigo Bissacot, Eric O. Endo, and Satoshi Handa.

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(12h-13h) Speaker: Yvan Velenik (Université de Genève)

Title: Ferrari–Spohn asymptotics for an Ising model interface (SLIDES) (VIDEO)


Abstract: After briefly reviewing some of the known results about (diffusive) scaling limits of interfaces in the 2d Ising model, I'll turn to a discussion of critical prewetting and explain our recent result that the scaling limit of a layer of unstable phase is a Ferrari-Spohn diffusion.


More precisely, I'll consider a 2d Ising model in square box of sidelength N, with a boundary condition enforcing the coexistence of the + phase inside the bulk of the system with a layer of - phase along one side. I'll then analyze the effect of a positive magnetic field of order 1/N on the behavior of the layer of unstable - phase.


This is based on joint work with Dmitry Ioffe, Sébastien Ott and Senya Shlosman.


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Organizers:

Contact: ising100years@gmail.com, rodrigo.bissacot@gmail.com, rsfreirejr@gmail.com

Sponsors: