Potential between adjoint sources in arbitrary representations

The potential between sources in arbitrary representations of the gauge group is studied on an anisotropic lattice in a spherical model approximation. It is shown analytically that for half-integer $j$ and $j'$ in the confinement phase the potential rises linearly, whereas for integer $j$ and half-integer $j'$ it rises infinitely which means a strong suppression of the combination of such states . For integer $j$ and $j'$ the potential shows Debay screening and Coulomb behavior in the deconfinement phase >. It is also shown, that $<\chi^{(j)}> \backsim <\chi>^{2j}$ when $<\chi> \gtrsim1$ and is in agreement with the mean field theory prediction, and $<\chi^{(j)}> \backsim <\chi>$ for $<\chi> \lesssim1$ which agrees with MC experiment. String tension model-computed for sources invariant under center group transformations demonstrates Casimir scaling in the intermediate distance regime and turns into zero at large distances.