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

Abstract

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 $T\to 0$ at the percolation threshold the Potts thermal exponent ${\nu }_T$ equals the percolation exponent ${\nu }_p$, implying a crossover exponent $\phi =1\mathrm{}$, for any $s$ and $d$. For the $n$-vector model ($n>\mathrm{}1\mathrm{}$), ${\nu }_T=\frac{{\nu }_p}{{\zeta }_R}$, where ${\zeta }_R$ is a resistivity critical exponent. Agreement with recent experiments for two-dimensional dilute Ising and Heisenberg systems is excellent.