Critical Dynamics at the Percolation Threshold by Fractal and Scaling Approaches

Abstract

The critical dynamics of Heisenberg spin systems at the percolation threshold is obtained from the transformation of the equations of motion under a length scaling acheived by climination of sites. The method is applied exactly to $d$-dimensional nonrandom fractals representing the infinite-cluster backbone and approximatcly to a truly random twodimensional system to yield dynamic scaling forms for response function and characteristic frequency, and associated static and dynamic critical exponents.