Non-perturbative states in the 3D phi(4) theory

We show that the spectrum of the three-dimensional phi(4) theory in the bro ken symmetry phase contains non-perturbative states. We determine the spect rum using a new variational technique based on the introduction of operator s corresponding to different length scales. The presence of non-perturbativ e states accounts for the discrepancy between Monte Carlo and perturbative results for the universal ratio xi/xi(2nd) We introduce and study some univ ersal amplitude ratios related to the overlap of the spin operator with the states of the spectrum. The analysis is performed for the phi(4) theory re gularized on a lattice and for the Ising model. This is a nice verification of the fact that universality reaches far beyond critical exponents. Final ly, we show that the spectrum of the model, including non-perturbative stat es, accurately matches the glueball spectrum in the Z(2) gauge model, which is related to the Ising model through a duality transformation, (C) 1999 P ublished by Elsevier Science B,V, All rights reserved.