M.V. Kompaniets (SPbU)

 

Multiloop calculations in models of critical behavior and stochastic turbulence

 

With renormalization group approach we investigate models of critical behavior and stochastic turbulence. We present approach that allows to express anomalous dimensions through renormalized Green functions for which it is possible to write a representation suitable for direct numerical calculations. In the framework of this approach we calculated critical exponents in various models of critical behavior. In the model of the stochastic turbulence we developed a new technique for calculation of the Kolmogorov constant which allows to improve significantly convergence of the perturbation series. Also the limit of large space dimensions ($d\to\infty$) for this model was considered. It is supposed that in the framework of the 1/d expansion it is possible to solve the problem of the anomalous scaling. Results of the recent six loop analytic calculations of the anomalous dimensions and beta function of the $\phi^4$ model are presented as well