  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.
