Vortex critical behavior at the deconfinement phase transition

The deconfinement phase transition in SU~2! Yang-Mills theory is reexamined in the vortex picture. Defining the world sheets of the confining vortices by maximal center projection, the percolation properties of the vortex lines in the hypercube consisting of the time axis and two spatial axes are studied. Using the percolation cumulant, the temperature for the percolation transition is found to be in good agreement with the critical temperature of the thermal transition. The finite size scaling function for the cumulant is obtained. The critical index of the finite size scaling function is consistent with the index of the 3D Ising model.