Correction induced by irrelevant operators in the correlators of the two-dimensional Ising model in a magnetic field

We investigate the presence of irrelevant operators in the two-dimensional Ising model perturbed by a magnetic field, by studying the corrections indu ced by these operators in the spin-spin correlator of the model. To this en d we perform a set of high-precision simulations for the correlator both al ong the axes and along the diagonal of the lattice. By comparing the numeri cal results with the predictions of a perturbative expansion around the cri tical point we find unambiguous evidence 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 + (T) over bar (2), which accounts for the breaking of the rotational invariance due to the la ttice. This result agrees with what was already known for the correlator ev aluated exactly at the critical point and also with recent results obtained in the case of the thermal perturbation of the model.