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 T→0 at the percolation threshold the Potts thermal exponent νT equals the percolation exponent νₚ, implying a crossover exponent φ=1, for any s and d. For the n-vector model ($n>1$), νT=νₚζR, where ζR is a resistivity critical exponent. Agreement with recent experiments for two-dimensional dilute Ising and Heisenberg systems is excellent.