A method is suggested for calculating the critical temperature in
multicomponent field theory with weak interactions. The method is based on
self-similar approximation theory allowing for the extrapolation of series in
powers of asymptotically small coupling to finite and even infinite couplings.
The extrapolation for the critical temperature employs self-similar factor
approximants. The found results are in perfect agreement with Monte Carlo
simulations.Comment: Latex file, 10 page
