Violation of finite-size scaling in the spherical limit of the rho(4) theory

We derive exact results of thermodynamic quantities of the O(n) symmetric p hi(4) theory in the limit n --> infinity both for the bulk with external fi eld h and in a finite d-dimensional hypercubic geometry with periodic bound ary conditions at h = 0. Universal bulk scaling is verified in the asymptot ic region of the h-T plane. For the finite system, however, we show that fi nite-size scaling is violated in the region L >> zeta where L is the size o f system and zeta is the bulk correlation length above T-c. (C) 2000 Elsevi er Science B.V. All rights reserved.