Correction induced by irrelevant operators in the correlators of the 2d Ising model in a magnetic field

TL;DR

This study uses high-precision simulations to identify and analyze the effects of irrelevant operators on the spin-spin correlator in the 2d Ising model under a magnetic field, revealing the dominant role of the spin 4 operator.

Contribution

It provides the first detailed numerical evidence of irrelevant operators affecting correlators in the 2d Ising model with a magnetic field, especially highlighting the spin 4 operator's significance.

Findings

Irrelevant operators induce measurable corrections in correlators.

The spin 4 operator T^2 + ar T^2 dominates the correction effects.

Results confirm the breaking of rotational invariance due to lattice effects.

Abstract

We investigate the presence of irrelevant operators in the 2d Ising model perturbed by a magnetic field, by studying the corrections induced by these operators in the spin-spin correlator of the model. To this end we perform a set of high precision simulations for the correlator both along the axes and along the diagonal of the lattice. By comparing the numerical results with the predictions of a perturbative expansion around the critical point we find unambiguous evidences of the presence of such irrelevant operators. It turns out that among the irrelevant operators the one which gives the largest correction is the spin 4 operator T^2 + \bar T^2 which accounts for the breaking of the rotational invariance due to the lattice. This result agrees with what was already known for the correlator evaluated exactly at the critical point and also with recent results obtained in the case of the thermal perturbation of the model.