Confinement-deconfinement order parameters

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.