A finite temperature study of the (2 + 1) Abelian Higgs model

We study the phase diagram of the finite temperature (2 + 1) Abelian Higgs model. We observe, for low values of the quartic scalar self-coupling, the existence of three phases separated by two lines. We study, in detail, the nature of the U(1) deconfining phase transition extension line in the limit of low values of the hopping parameter K for each temperature, and verify that in that limit the behaviour of this line is similar to that of the pure U(1) theory. (author)