Non-perturbative states in the 3D φ4 theory Original Research Article

We show that the spectrum of the three-dimensional φ4 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 ξ/ξ2nd. 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 φ4 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 Z2 gauge model, which is related to the Ising model through a duality transformation.