Anomalous exponents to order ɛ3 in the rapid-change model of passive scalar advection

Field-theoretic renormalization group is applied to the Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance <v(t,x)v(t',x)>- <v(t,x)v(t',x')>~δ(t- t')\|x-x'\|^ɛ. Inertial-range anomalous exponents, related to the scaling dimensions of tensor composite operators built of the scalar gradients, are calculated to the order ɛ³ of the ɛ expansion. The nature and the convergence of the ɛ expansion in the models of turbulence are briefly discussed.