Nonperturbative zero modes in the Kraichnan model for turbulent advection

The anomalous scaling behavior of the nth order correlation functions ${\mathrm{F}}_{\mathrm{n}}$ of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero modes) of the Kraichnan equation B-|${\mathrm{Ax}}_{\mathrm{n}}$ ${\mathrm{F}}_{\mathrm{n}}$=0. Previous analysis found zero modes in perturbation theory with respect to a small parameter. We present a computer-assisted analysis of the simplest nontrivial case of n=3: we demonstrate nonperturbatively the existence of anomalous scaling, and compare the results with the perturbative predictions.