The effective field theory approach to high temperature field theory can be
used to study the phase transition in theories with spontaneously broken s
ymmetry. I construct a sequence of two effective three-dimensional field th
eories which are valid on successively longer distance scales for a specifi
c model: N charged scalars coupled to a U(1) gauge field. The resulting eff
ective Lagrangian can be used to investigate the phase transition, in parti
cular the order of the phase transition as a function of N, using lattice s
imulations. [S0556-2821(98)03624-8].