BICRITICAL MACROSCOPIC CONDUCTIVITY EXPONENT IN DIMENSIONALITIES 2, 3 AND INFINITY

The authors present values of the bicritical macroscopic conductivity exponent nu , which was recently defined for the random resistor lattice. For dimensionality D=2, the value is obtained exactly by exploiting the properties of the dual lattice. In three dimensions a potential problem is solved approximately on a 34*34*34 computer-simulated cubic lattice. For infinite dimensionality, the exponent is extracted by treating the Cayley tree lattice. The authors find: nu (D=2)=0(exact); nu (D=3)=0.78+or-0.10; nu (D= infinity )=2(exact). Knowledge of the nu exponent is shown to be a necessary prerequisite for a complete understanding of the critical behaviour of multiphase inhomogeneous conducting systems.