Two-dimensional multicomponent Abelian-Higgs lattice models

TL;DR

This paper investigates the critical behavior of the two-dimensional multicomponent Abelian-Higgs lattice model, revealing its universal features are governed by the 2D CP(N-1) field theory at zero temperature.

Contribution

It provides a numerical analysis of the finite-size scaling in the zero-temperature limit, connecting the model's renormalization-group flow to the CP(N-1) universality class.

Findings

Disordered phase at finite temperature consistent with Mermin-Wagner theorem

Critical behavior only at zero temperature

Universal features governed by the 2D CP(N-1) field theory

Abstract

We study the two-dimensional lattice multicomponent Abelian-Higgs model, which is a lattice compact U(1) gauge theory coupled with an N-component complex scalar field, characterized by a global SU(N) symmetry. In agreement with the Mermin-Wagner theorem, the model has only a disordered phase at finite temperature and a critical behavior is only observed in the zero-temperature limit. The universal features are investigated by numerical analyses of the finite-size scaling behavior in the zero-temperature limit. The results show that the renormalization-group flow of the 2D lattice N-component Abelian-Higgs model is asymptotically controlled by the infinite gauge-coupling fixed point, associated with the universality class of the 2D CP(N-1) field theory.