**Authors:**
Alessandro Giuliani, Vieri Mastropietro

**Title:** *
Universal
finite size corrections and the central charge in non solvable
Ising models
*

**Abstract: **
We investigate a non solvable two-dimensional ferromagnetic
Ising model with nearest neighbor plus weak finite range
interactions of strength λ. We rigorously establish one of the
predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature
the finite size corrections to the free energy
are universal, in the sense that they are exactly independent of the interaction. The
corresponding central charge, defined in terms of the coefficient of the first subleading term to the free
energy,
as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2
for all 0≤λ≤λ_{0} and λ_{0} a small but finite convergence
radius.
This is one of the very few cases where the predictions of CFT can be rigorously
verified starting from a microscopic non solvable statistical model. The proof
uses a combination of rigorous renormalization group methods with
a novel partition function inequality, valid for ferromagnetic interactions.

**Keywords:**
2D Ising model, non-integrable models, central charge, finite volume corrections,
universality, conformal field theory,
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

Vieri Mastropietro

Dipartimento di Matematica

Università di Milano

Via Saldini, 50, I-20133 Milano - ITALY

e-mail: Vieri DOT Mastropietro AT unimi DOT it