s-State potts model on a Cayley tree

The Potts model is shown to exhibit a phase transition of continuous order on a Cayley tree. The leading nonanalytic part of the free energy ∣L∣ ^$\text{K}$_s involves a critical exponent $\text{K}$_s going from one to infinity as the coupling goes f rom infinity to K_BP, the Bethe-Peierls critical coupling.