Non-perturbative states in the 3D phi⁴ theory

We show that the spectrum of the three dimensional phi^4 theory in the broken symmetry phase contains non-perturbative states. We determine the spectrum using a new variational technique based on the introduction of operators corresponding to different length scales. The presence of non-perturbative states accounts for the discrepancy between Monte Carlo and perturbative results for the universal ratio xi/xi_2nd. We introduce and study some universal 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 regularized on a lattice and for the Ising model. This is a nice verification of the fact that universality reaches far beyond critical exponents. Finally, we show that the spectrum of the model, including non-perturbative states, accurately matches the glueball spectrum in the Z(2) gauge model, which is related to the Ising model through a duality transformation.