  The vortex free energy is studied in the random vortex world-surface model of
the infrared sector of SU(3) Yang-Mills theory. The free energy of a center
vortex extending into two spatial directions, which is introduced into
Yang-Mills configurations when acting with the 't Hooft loop operator, is
verified to furnish an order parameter for the deconfinement phase transition.
It is shown to exhibit a weak discontinuity at the critical temperature,
corresponding to the weak first order character of the transition.
