Critical Temperature in Weakly Interacting Multicomponent Field Theory

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.