The turbulent Prandtl number has been calculated in the two-loop approximation of the ε expansion of the stochastic theory of turbulence. The strikingly small value obtained for the two-loop correction explains the good agreement of the earlier one-loop result with the experiment. This situation is drastically different from other available nontrivial two-loop results, which exhibit corrections of the magnitude of the one-loop term. The reason is traced to the mutual cancellation of additional divergences appearing in two dimensions which have had a major effect on the results of previous calculations of other quantities.
We perform the Borel resummation of the currently known terms of the ε-expansion up to order ε 4 of the dynamical exponent z in the critical-behavior model A. We obtain the large-order asymptotic approximation of the ε-expansion of the dynamical exponent and find a significant discrepancy between the currently calculated orders of the expansion and the obtained asymptotic values. We discuss the influence of this deviation on the accuracy of the resummation results.
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