FM 3-2012 (arXiv:1204.4040)

Authors: Alessandro Giuliani, Rafael L. Greenblatt, Vieri Mastropietro

Title: The scaling limit of the energy correlations in non integrable Ising models
 
Abstract: We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength λ, in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one. Our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory, which generalizes the one originally used by Schultz, Mattis and Lieb for the nearest neighbor Ising model. The interacting model is then analyzed by a multiscale method first proposed by Pinson and Spencer. If the lattice spacing is finite, then the correlations cannot be computed in closed form: rather, they are expressed in terms of infinite, convergent, power series in λ. In the scaling limit, these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable Ising model, up to a finite renormalization of the parameters. Explicit bounds on the speed of convergence to the scaling limit are derived.

Keywords: 2D Ising model, non-integrable models, scaling limit, fermionization, bosonization, universality, renormalization group

Alessandro Giuliani
Dipartimento di Matematica
Università di Roma Tre
L.go S. Leonardo Murialdo 1, 00146 Roma - Italy
e-mail: giuliani AT mat DOT uniroma3 DOT it

Rafael Greenblatt
Dipartimento di Matematica
Università di Roma Tre
L.go S. Leonardo Murialdo 1, 00146 Roma - Italy
e-mail: rafael DOT greenblatt AT gmail DOT com

Vieri Mastropietro
Dipartimento di Matematica
Università di Roma Tor Vergata
V.le della Ricerca Scientifica 1, 00133 Roma - Italy
e-mail: mastropi AT mat DOT uniroma2 DOT it