Bloch walls and anomalous longitudinal Glauber dynamics of dilute anisotropic magnets at the percolation threshold.

Abstract

The relaxational dynamics of the d-dimensional, classical anisotropic Heisenberg (Ising-Heisenberg) model near the percolation bicritical point (p=${p}_{c}$, T=0) is considered. As in the corresponding Ising system, the relevant physical process involves the activation of domain walls over a hierarchy of energy barriers. In this system the domain boundaries are quasi-one-dimensional Bloch walls and we show that a simple scaling theory gives exact results for the Bloch-wall energy and length across the whole range of anisotropy. These results are used to derive explicit expressions for the characteristic time ${\ensuremath{\tau}}_{c}$ in the various scaling regimes of interest. In particular, it is found that the conventional dynamic scaling hypothesis for ${\ensuremath{\tau}}_{c}$ is violated at sufficiently low temperatures in all cases of nonvanishing anisotropy, and the crossover to singular dynamic scaling behavior is demonstrated explicitly.