M. V. Kompaniets

Six loop analytical calculation of the field anomalous dimension and the critical exponent η in O ( n )-symmetric φ 4 model

Abstract We report on a completely analytical calculation of the field anomalous dimension γ φ and the critical exponent η for the O ( n ) -symmetric φ 4 model at the record six loop level. We successfully compare our result for γ φ with n = 1 with the predictions based on the method of the Borel resummation combined with a conformal mapping (Kazakov et al., 1979 [40] ). Predictions for seven loop contribution to the field anomalous dimensions are given.

RENORMALIZATION-GROUP APPROACH TO THE STOCHASTIC NAVIER–STOKES EQUATION: TWO-LOOP APPROXIMATION

The field theoretic renormalization group is applied to the stochastic Navier--Stokes equation that describes fully developed fluid turbulence. The complete two-loop calculation of the renormalization constant, the

Renormalization group in the infinite-dimensional turbulence: third-order results

\beta

Five-loop numerical evaluation of critical exponents of the phiv4 theory

function, the fixed point and the ultraviolet correction exponent is performed. The Kolmogorov constant and the inertial-range skewness factor, derived to second order of the

Anomalous scaling of a passive vector field in d dimensions: higher order structure functions

\eps

H-model of critical dynamics: Two-loop calculations of RG functions and critical indices

expansion, are in a good agreement with the experiment. The possibility of the extrapolation of the

Critical behaviour of the O(n)-ϕ4 model with an antisymmetric tensor order parameter

\eps

Critical behavior of the O ( n ) ϕ 4 model with an antisymmetric tensor order parameter: Three-loop approximation

expansion beyond the threshold where the sweeping effects become important is demonstrated on the example of a Galilean-invariant quantity, the equal-time pair correlation function of the velocity field. The extension to the

Renormalization-group investigation of a superconducting U( r )-phase transition using five loops calculations

d

Some specific features of the ε expansion in the theory of turbulence and the possibility of its improvement

-dimensional case is briefly discussed.