On the Short Distance Behavior of the Critical Ising Model Perturbed by a Magnetic Field

TL;DR

This paper develops a method to compute short-distance corrections in the 2D critical Ising model under a magnetic field, revealing fractional powers and providing estimates for the energy operator's VEV.

Contribution

It introduces a novel approach using O.P.E. Wilson coefficients and Mellin transforms to analyze perturbations in the Ising model, capturing fractional powers of the magnetic field.

Findings

Derived all-order IR-safe formulas for correlator corrections

Identified fractional powers of magnetic field in the expansion

Estimated the vacuum expectation value of the energy operator

Abstract

We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with O.P.E. Wilson coefficients instead of correlators, all order I.R. safe formulas can be obtained for the perturbative expansion with respect to magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, that are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform have been used to compute the I.R. behavior of the regularized integrals. As a corollary of our results, by comparing the existing numerical data for the lattice model we give an estimate of the Vacuum Expectation Value of the energy operator, left unfixed by usual nonperturbative approaches (Thermodynamic Bethe Ansatz).