The breakdown of dynamic scaling of the bond-diluted Ising model at the percolation threshold for hypercubic lattices

Abstract

The authors use real-space renormalisation group techniques to study the kinetic Ising model (with Glauber dynamics) on bond-diluted d-dimensional hypercubic lattices, at the percolation threshold. The results confirm and generalise the recently proposed breakdown of dynamic scaling and they predict a dependence on dimensionality of the factors A and B on the temperature-dependent dynamic exponent z=A log xi +B (where xi is the thermal correlation length). These factors also depend on the lattice scaling factor (b); the authors suggest that the limit b=1 may be taken as the best choice for the important coefficient A, leading to A=d(d-1)/2 nu p.