Percolation thresholds in Ising magnets and conducting mixtures

The effect of the percolation threshold on conduction in mixtures and on the magnetic ordering temperature in alloys of high- and low- TC material is described using a real-space rescaling approximation (introduced by Kadanoff, following an idea of Migdal) which is applicable to systems of arbitrary spatial dimensionality d. We calculate exponents describing the regimes just above and just below pc for the case of bond dilution in resistor networks or Ising ferromagnets. The results are accurate for d=2 in those cases where comparison is possible and qualitatively correct for d=3, but are invalid in the limit d→. Ising spin glasses do not show order in 2 dimensions, in this approximation, but may do so in 3 dimensions. © 1977 The American Physical Society.