23/06/2021, 17:00 — 18:00 — Online
Yvan Velenik, Université de Genève
Failure of the Ornstein-Zernike asymptotics for the pair correlation function at high temperature and small density
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.
