SBP: Failure of the Ornstein--Zernike asymptotics for the... - Yvan Velenik, Université de Genève

Seminário Brasileiro de Probabilidade
Palestrante: Yvan Velenik, Université de Genève
Titulo: Failure of the Ornstein--Zernike asymptotics for the pair correlation function at high temperature and small density

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.

Apoio:
- IMPA
- Instituto Superior Técnico de Lisboa
- UFBA
- UFMG
- UFRGS
- UFRJ
- Unicamp
- Universidade do Porto
- USP

Comitê científico:
- Luiz Renato Fontes (USP)
- Tertuliano Franco (UFBA)
- Nancy Lopes Garcia (Unicamp)
- Patrícia Gonçalves (IST, Lisboa)
- Marcelo Hilário (UFMG)
- Roberto Imbuzeiro (Coordenador, IMPA)
- Claudio Landim (Coordenador, IMPA)
- Adriana Neumann (UFRGS)
- Serguei Popov (UP, Porto)
- Glauco Valle (UFRJ)

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