Finite-Size Scaling in the $O(N)$ ${\varphi }_4^4$ Model

Abstract

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 $O(n)$ ${\varphi }^4$ 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.

13 pages