The Ornstein-Zernike theory is a heuristic picture describing the behaviour of correlation functions in high temperature/low density systems. It gives a prediction for the asymptotic behaviour of the (truncated) two-point function: $G(0,x) = c|x|^{-(d-1)/2}e^{-nu(x)}(1+o(1))$ where nu is a norm on $R^d$.
While the OZ picture was made rigorous in various situations, it was recently realized that the belief that the asymptotics holds generically in systems with a finite correlation length was misplaced: indeed the OZ asymptotics can be shown to fail for various systems with exponentially decaying interactions at very high temperature or very low density.
In this talk, I will focus on the example of the ferromagnetic Ising model and will review the recent progresses towards the description of the fine asymptotics of G when $T>T_c$ and the interaction is exponentially decaying.
Based on joint work with Y. Aoun, D. Ioffe, and Y. Velenik.

Il seminario avrà luogo in presenza presso il Dipartimento di Matematica e Fisica, Sezione di Matematica,
L.go S. L. Murialdo 1 - Aula 211
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org: GIULIANI Alessandro