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Mathematical Physics Seminar

Alessandro Giuliani - 2D Ising models with finite range interactions: scaling limit of the critical theory

Alessandro Giuliani

Location:  Webinar
Date & time: Thursday, 30 July 2020 at 11:00AM - 12:00PM

Alessandro Giuliani – University of Roma Tre

Thursday, July 30, 11:00AM

“2D Ising models with finite range interactions: scaling limit of the critical theory”

We consider finite range perturbations of the 2D Ising model in cylindrical geometry. We show that at Tc the rescaled multipoint energy correlations converge to a well defined limit as the lattice mesh tends to zero. This scaling limit is the same as the one for nearest neighbor Ising, up to a finite multiplicative renormalization constant, independent of the shape of the domain. The proof is based on a representation of the generating function of correlations in terms of a non-Gaussian Grassmann integral, and a constructive Renormalization Group analysis thereof. Two novelties, compared with previous works, are: (1) proof that the scaling dimension of boundary operators is better by one dimension than their bulk counterparts; (2) control of the marginal boundary terms, thanks to a cancellation mechanism based on an approximate image rule for the fermionic Green's function. Based on joint works with G. Antinucci, R. Greenblatt and V. Mastropietro.

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