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 ${\tau }_c$ in the various scaling regimes of interest. In particular, it is found that the conventional dynamic scaling hypothesis for ${\tau }_c$ is violated at sufficiently low temperatures in all cases of nonvanishing anisotropy, and the crossover to singular dynamic scaling behavior is demonstrated explicitly.

• Received 8 October 1986

DOI:https://doi.org/10.1103/PhysRevB.38.11755