  We obtain an explicit expression for the multipoint energy correlations of a
non solvable two-dimensional Ising models with nearest neighbor ferromagnetic
interactions plus a weak finite range interaction of strength $\lambda$, in a
scaling limit in which we send the lattice spacing to zero and the temperature
to the critical one. Our analysis is based on an exact mapping of the model
into an interacting lattice fermionic theory, which generalizes the one
originally used by Schultz, Mattis and Lieb for the nearest neighbor Ising
model. The interacting model is then analyzed by a multiscale method first
proposed by Pinson and Spencer. If the lattice spacing is finite, then the
correlations cannot be computed in closed form: rather, they are expressed in
terms of infinite, convergent, power series in $\lambda$. In the scaling limit,
these infinite expansions radically simplify and reduce to the limiting energy
correlations of the integrable Ising model, up to a finite renormalization of
the parameters. Explicit bounds on the speed of convergence to the scaling
limit are derived.
