Thermal Phase Transition of the Dilutes-State Potts andn-Vector Models at the Percolation Threshold

A general theory is given for the quenched dilute s-state Potts and n-vector models in any dimension d. It is shown that for T0 at the percolation threshold the Potts thermal exponent ₓ equals the percolation exponent ₏, implying a crossover exponent =1, for any s and d. For the n-vector model (n>1), ₓ={₏}{ₑ}, where ₑ is a resistivity critical exponent. Agreement with recent experiments for two-dimensional dilute Ising and Heisenberg systems is excellent.