Finite-Size Scaling in the $O(N)$ $\phi^4_4$ 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 ) φ 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.