**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