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Mathematical Physics Seminar

Vieri Mastropietro - Lines of critical points and Kadanoff relations

Vieri Mastropietro – University of Milan

Location:  zoom
Date & time: Wednesday, 13 January 2021 at 10:45AM - 11:45AM

Vieri Mastropietro – University of Milan

Wednesday, January 13, 10:45AM

Title:
"
Lines of critical points and Kadanoff relations "

In a wide class of planar statistical mechanics models, including coupled Ising, Vertex, Ashkin-Teller or interacting dimer models there are continuously varying exponents. Kadanoff (PRL 39, 15,904, 1977) introduced a notion of universality, proposing relations allowing their determination in terms of a single one of them. In particular, he proposed X_p=X_e/4 and X_C X_e=1 (eq 13a and 13b). The second relation involves local expressions and it has been proved in collaboration with Benfatto and Falco (CMP 292, 569 (2009)) in a wide class of systems including solvable and not solvable models. The first involves extended quantities and it is quite elusive. In a recent paper with Giuliani and Toninelli (CMP 377(3), 1883-1959, 2020) it was considered a class of interacting dimer models (solvable or not solvable) and it was proved an universal relation for extended quantities eta=A connecting the variance of the height function with the exponent of dimer correlations. For a special choice of parameters it reduces to the (13a) relation of Kadanoff for the Ashkin -Teller model.