Broken phase of the 4-dimensional Ising model in a finite volume

The volume dependence of physical quantities, like renormalized mass and coupling, is numerically investigated in the broken phase of the 4-dimensional Ising model. It is shown that finite volume effects in small and intermediate volumes are dominated by vacuum tunneling. The tunneling phenomenon is investigated in detail. The splitting of the ground states due to tunneling turns out to be given to a good approximation by an instanton-like calculation. The large volume limit of the physical quantities is compared to the prediction of the perturbative renormalization group which connects the scaling behaviour on both sides of the phase transition. A good agreement with the 3-loop β-function is observed. (orig.)