Title of the talk: "The theory without divergences. What is this?"

Speaker: Svetlana E. Vorobyeva, The Dept. of Statisticel Physics

Abstract

Method of renormalization group and the $\epsilon$-expansion is
generally recognized method of critical exponents calculation in
the theory of critical phenomena. The usual way of their
determination is associated with renormalization constants calculation.

This method is successfully used in the analytical calculation of the
static Feynman diagrams. In critical dynamics problems such calculations
are faced with considerable difficulties.

The numerical method of computation is complicated by the fact that the
renormalization constants are singular functions of the parameter $\epsilon$.
We formulate an approach for finding the anomalous dimensions, bypassing the
calculation of renormalization constants ("theory without divergences" in
the terminology of A. Zavyalov). For the calculation of multiple integrals
we use the method Sector Decomposition, modified with reference to problems
of critical dynamics. The calculations in the A-model of critical dynamics
and the model of percolation were carried out.