  The aim of this paper is to determine the behavior of the specific heat of
the 4-dimensional Ising model at the critical temperature, and via that
determine if the Ising model and the $\phi^4$-model belong to the same
universality class in dimension 4. In order to do this we have carried out what
is currently the largest scale simulations of the 4-dimensional Ising model,
extending the lattices size up to $L=256$ and the number of samples per size by
several orders of magnitude compared to earlier works, keeping track of data
for both the canonical and microcanonical ensembles. Our conclusion is that the
Ising model has a bounded specific heat, while the $\phi^4$-model is known to
have a logarithmic divergence at the critical point. Hence the two models
belong to distinct universality classes in dimension 4.
