Violation of finite-size scaling in the spherical limit of the ϕ4 theory

Abstract

We derive exact results of thermodynamic quantities of the O( n) symmetric ϕ 4 theory in the limit n→∞ both for the bulk with external field h and in a finite d-dimensional hypercubic geometry with periodic boundary conditions at h=0. Universal bulk scaling is verified in the asymptotic region of the h– T plane. For the finite system, however, we show that finite-size scaling is violated in the region L⪢ ξ where L is the size of system and ξ is the bulk correlation length above T c.