Confinement-deconfinement order parameters

TL;DR

This paper numerically investigates a monopole creation operator in a 3D model, demonstrating its effectiveness in distinguishing phases with different monopole condensations in the Abelian Higgs model.

Contribution

It introduces a numerical analysis of a monopole creation operator using Mandelstam strings, showing its ability to differentiate phases in the Abelian Higgs model.

Findings

The operator discriminates between condensed and non-condensed monopole phases.

Mandelstam strings effectively imitate Coulombic magnetic fields.

Condensation of Mandelstam strings correlates with phase distinctions.

Abstract

We study numerically the monopole creation operator proposed recently by Frohlich and Marchetti. The operator is defined with the help of a three dimensional model which generates random Mandelstam strings. These strings imitate the Coulombic magnetic field around the monopole. We show that if the Mandelstam strings are condensed the creation operator discriminates between the phases with condensed and non--condensed monopoles in the Abelian Higgs model with the compact gauge field.