PHASE TRANSITION OF N-COMPONENT SUPERCONDUCTORS

TL;DR

This paper studies the phase transition types in a three-dimensional abelian Higgs model with N complex scalars, revealing how the transition order depends on coupling ratios and analyzing critical behavior across different N values.

Contribution

It provides a non-perturbative analysis of the phase transition in the abelian Higgs model using the gauge-invariant average action and explores the fixed points and critical exponents for various N.

Findings

Transition can be first- or second-order depending on coupling ratios.

Poor convergence of xpansion results for =1, even at large N.

Existence of a parameter range with second-order transition for all N.

Abstract

We investigate the phase transition in the three-dimensional abelian Higgs model for N complex scalar fields, using the gauge-invariant average action \Gamma_{k}. The dependence of \Gamma_{k} on the effective infra-red cut-off k is described by a non-perturbative flow equation. The transition turns out to be first- or second-order, depending on the ratio between scalar and gauge coupling. We look at the fixed points of the theory for various N and compute the critical exponents of the model. Comparison with results from the \epsilon-expansion shows a rather poor convergence for \epsilon=1 even for large N. This is in contrast to the surprisingly good results of the \epsilon-expansion for pure scalar theories. Our results suggest the existence of a parameter range with a second-order transition for all N, including the case of the superconductor phase transition for N=1.