THE LONG-RANGE INTERACTION IN MASSLESS (λΦ4)4 THEORY

Does massless (lambda Phi(4))(4) theory exhibit spontaneous symmetry breaking (SSB)? The raw one-loop result implies that it does, but the RG-improved result implies the opposite. We argue that the appropriate low-energy effective theory is an on local field theory involving an attractive, long-range interaction Phi(2)(x)Phi(2)(y)/vertical bar x-y vertical bar(4). RG improvement then requires running couplings for both this interaction and the original point like interaction. A crude calculation in this framework yields SSB even after RG improvement and closely agrees with the raw one-loop result.