Phase Transitions in a Scalar Theory in 2+1 Dimensions

摘要

We consider a renormalizable quantum field theory for a single scalar field in 2+1 dimensions at finite temperature with a Z_2 symmetry. We discuss the infrared pathologies of this theory and propose a method of resummation through the use of a gap equation. We present some numerical results for the effective potential that show that the Z_2 symmetry is broken at low temperatures, but is restored at high temperature by a first-order phase transition.