Título: Long-range Ising model and decaying fields- a contour approach

Palestrante: Lucas Affonso (IME-USP)
Data: 28/06/2021
Horário: 15:00h
Local: Transmissão online.

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Resumo: In 1982, Fröhlich and Spencer solved a long-standing conjecture about phase transition in a one-dimensional long-range Ising model for 1/r^2 interaction energy. After that, Cassandro, Ferrari, Merola, and Presutti extended the contour argument for other decays \alpha. In this talk, we address the multidimensional long-range Ising model, showing that a contour argument holds for all decays \alpha> d. As an application, we will show how our techniques can be used to study phase transition when the model has a decaying magnetic field.

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

All the talks are held in English.

The videos of the online seminars held in 2020 are available at HERE. 

For the 2021 series, a few days after each meeting the video should be available at HERE. 

Título: The Ant Random Walk

Palestrante: Guilherme Reis (UFBA)
Data: 21/06/2021
Horário: 15:00h
Local: Transmissão online.

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Resumo: The Ant RW belongs to the class of random walks with reinforcement. Our goal is to observe through this stochastic process the ant mill phenomenon: the walker is eventually trapped in a circuit of the graph which will be followed forever. In recent work we show that this phenomenon can be observed with weaker assumptions in the reinforcement function. Ours inspiration is the ant mill phenomenon in which a group of army ants are separated from the main group, lose the pheromone track and begin to follow one another, forming a continuously rotating circle. The ants are not able to go back home and will eventually die of exhaustion as we can see in the video "Why army ants get trapped in ‘death circles’" on YouTube.

Works in collaboration with Dirk Erhard and Tertuliano Franco.

All the talks are held in English.

The videos of the online seminars held in 2020 are available at HERE.

For the 2021 series, a few days after each meeting the video should be available at HERE.

Título: Failure of the Ornstein--Zernike asymptotics for the pair correlation function at high temperature and small density

Palestrante: Yvan Velenik, Université de Genève
Data: 23/06/2021
Horário: 13:00h
Local: Transmissão online.

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ID da reunião: 958 0581 3232

Resumo: After briefly reviewing what is known about the long-distance asymptotic behavior of the 2-point function in lattice spin systems with finite-range interactions, I'll turn to the corresponding result for systems with interactions of infinite range. I'll show that, contrarily to standard expectations in Physics, the classical Ornstein-Zernike asymptotic formula for the 2-point function does not always hold, even in regimes where it was expected to, namely systems with interactions decaying exponentially fast at very high temperature and/or very low density. I'll explain how this is intimately related to the possible non analytic dependence of the correlation length in the relevant parameters (for instance, temperature), a phenomenon that can occur even in one-dimensional systems. This can be also related to a condensation transition in the graphical representations of these correlations. For simplicity, the focus will be on the Ising model, but most of the results hold much more generally. This is based on joint work with Yacine Aoun, Dmitry Ioffe and Sébastien Ott.

Título: Lozenge tilings and the Gaussian free field on a cylinder

Palestrante: Marianna Russkikh, MIT
Data: 16/06/2021
Horário: 13:00h
Local: Transmissão online.

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ID da reunião: 958 0581 3232

Resumo: We discuss new results on lozenge tilings on an infinite cylinder, which may be analyzed using the periodic Schur process introduced by Borodin. Under one variant of the $q^{vol}$ measure, corresponding to random cylindric partitions, the height function converges to a deterministic limit shape and fluctuations around it are given by the Gaussian free field in the conformal structure predicted by the Kenyon-Okounkov conjecture. Under another variant, corresponding to an unrestricted tiling model on the cylinder, the fluctuations are given by the same Gaussian free field with an additional discrete Gaussian shift component. Fluctuations of the latter type have been previously conjectured by Gorin for tiling models on planar domains with holes. This talk is based on joint work with Andrew Ahn and Roger Van Peski.