Convergence of perturbation series for renormalization constants in Kraichnan model with "frozen" velocity field

TL;DR

This paper demonstrates that the perturbation series for renormalization constants in the Kraichnan model with a frozen velocity field converges, providing a calculated radius of convergence and analyzing the instanton solution.

Contribution

It establishes the convergence of the quantum-field perturbation expansion for the renormalization constant in the Kraichnan model with frozen velocity, including the calculation of its radius of convergence.

Findings

The perturbation series for Z_ν converges.

The radius of convergence was explicitly calculated.

An instanton solution was identified for the model.

Abstract

Instanton was found for Kraichnan model with 'frozen' velocity field. Large order asymptotic of quantum-field perturbation expansion for renormalization constant $Z_\nu$ was investigated. It was shown that this expansion is convergent one. The radius of convergence was calculated.