Revising the universality class of the four-dimensional Ising model

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.