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

TL;DR

This paper rigorously proves that in a non solvable 2D ferromagnetic Ising model with weak finite-range interactions, the finite size corrections to free energy at criticality are universal and the central charge remains constant at 1/2, confirming CFT predictions.

Contribution

It provides the first rigorous verification of CFT predictions for finite size corrections and central charge in a non solvable Ising model with weak interactions.

Findings

Finite size corrections are universal and interaction-independent.

Central charge remains constant at 1/2 for small interaction strengths.

Rigorous proof combines renormalization group methods with a novel partition function inequality.

Abstract

We investigate a non solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength \lambda. 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<\lambda<\lambda_0 and \lambda_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.