FM 12-2012 (arXiv:1211.3030)

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≤λ0 and λ0 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