Irrelevant operators in the two-dimensional Ising model

By using conformal-field theory, we classify the possible irrelevant operators for the Ising model on the square and triangular lattices. We analyze the existing results for the free energy and its derivatives and for the correlation length, showing that they are in agreement with the conformal-field theory predictions. Moreover, these results imply that the nonlinear scaling field of the energy-momentum tensor vanishes at the critical point. Several other peculiar cancellations are explained in terms of a number of general conjectures. We show that all existing results on the square and triangular lattice are consistent with the assumption that only nonzero spin operators are present.