Finite-Size Scaling in the O(N) φ⁴₄ Model

Perturbation theory and renormalization group methods are used to derive a finite-size scaling theory for the partition function zeroes and thermodynamic functions in the $O(n)$ $\phi^4$ model in four dimensions. The leading power--law scaling behaviour is the same as that of the mean field theory. There exist, however, multiplicative logarithmic corrections which are linked to the triviality of the theory.