Spin-spin correlations in finite systems: Scaling hypothesis and corrections to bulk behavior

We study the correlation function G(R,T;L) and the correlation length ξ(T;L) in a finite spherical model if size $L^{d\mathrm{-}d\mathcal{’}}$×${\infty }^{d\mathcal{’}}$ under periodic boundary conditions and emphasize the role of the variable L/ξ(L), rather than L/ξ(∞), as a natural scaling variable of the system throughout the transition region, including temperatures below $T_c$(∞). We obtain a variety of finite-size effects, some of which may have validity for all O(n) models with n>2.