Short distance behaviour of correlators in the 2D Ising model in a magnetic field

TL;DR

This paper investigates the short and long-distance behaviors of various correlators in the 2D Ising model under a magnetic field, comparing Monte Carlo simulations with theoretical approximations.

Contribution

It provides a detailed comparison between the Form Factor approach and a perturbative expansion, extending the latter to second order for improved accuracy.

Findings

Form Factor approach excels at larger distances.

Perturbative expansion is more accurate at short distances.

Extending the perturbative analysis improves agreement with simulations.

Abstract

We study the spin-spin, spin-energy and energy-energy correlators in the 2d Ising model perturbed by a magnetic field. We compare the results of a set of high precision Montecarlo simulations with the predictions of two different approximations: the Form Factor approach, based on the exact S-matrix description of the model, and a short distance perturbative expansion around the conformal point. Both methods give very good results, the first one performs better for distances larger than the correlation length, while the second one is more precise for distances smaller than the correlation length. In order to improve this agreement we extend the perturbative analysis to the second order in the derivatives of the OPE constants.