Effective Field Theory Approach to Phase Transitions

In this paper I discuss the effective field theory approach, recently developed by Braaten and Nieto in the investigation of quantum field theories at high temperature. I demonstrate that this method can be easily extended to the study of phase transitions in theories with spontaneous symmetry breaking. The first step consists of the construction of a sequence of two effective three-dimensional field theories, which are valid on successively longer distance scales. The second step in the study of the phase transition is using the second effective Lagrangian in either perturbatative calculations or lattice simulations. I apply the method to a theory which consists of $N$ charged U(N) symmetric scalars coupled to an Abelian gauge field. The effective Lagrangian can then be used on the lattice to investigate the order of the phase transition as a function of $N$.