  A finite-size scaling theory for the $\phi^4_4$ model is derived using
renormalization group methods. Particular attention is paid to the partition
function zeroes, in terms of which all thermodynamic observables can be
expressed. While the leading scaling behaviour is identical to that of mean
field theory, there exist multiplicative logarithmic corrections too. A
non-perturbative test of these formulae in the form of a high precision Monte
Carlo analysis reveals good quantitative agreement with the analytical
predictions.
