  Self-similar approximation theory is shown to be a powerful tool for
describing phase transitions in quantum field theory. Self-similar approximants
present the extrapolation of asymptotic series in powers of small variables to
the arbitrary values of the latter, including the variables tending to
infinity. The approach is illustrated by considering three problems: (i) The
influence of the coupling parameter strength on the critical temperature of the
O(N)-symmetric multicomponent field theory. (ii) The calculation of critical
exponents for the phase transition in the O(N)-symmetric field theory. (iii)
The evaluation of deconfinement temperature in quantum chromodynamics. The
results are in good agreement with the available numerical calculations, such
as Monte Carlo simulations, Pade-Borel summation, and lattice data.
