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Quenched and annealed Ising models on random graphs

Banff International Research Station for Mathematical Innovation and Discovery

The ferromagnetic Ising model is a paradigmatic model of statistical physics used to study phase transitions in lattice systems. In this talk I shall consider the setting where the regular spatial structure is replaced by a random graph, which is often used to model complex networks. I shall treat both the case where the graph is essentially frozen (quenched setting) and the case where instead it is rapidly changing (annealed setting). I shall prove that quenched and annealed may have different critical temperatures, provided the graph has sufficient inhomogeneity. I shall also discuss how universal results (law of large numbers, central limit theorems, critical exponents) are affected by the disorder in the spatial structure. The picture that I will present emerges from several joint works, involving V.H. Can, S. Dommers, C. Giberti, R.van der Hofstad and M.L.Prioriello.

Mathematics; Probability theory and stochastic processes; Statistics

video/mp4

Author affiliation: University of Modena and Reggio Emilia

2019-11-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72288

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/