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Critical Ising Spin Dynamics on Percolation Clusters

1985; American Physical Society; Volume: 54; Issue: 18 Linguagem: Inglês

10.1103/physrevlett.54.2030

1092-0145

Christopher L. Henley,

Opinion Dynamics and Social Influence

Ferromagnetically interacting Ising spins are placed on a fractal network (such as a critical percolation cluster) with ${T}_{c}=0$, and endowed with a single-spin-flip dynamics. At low temperatures the collective dynamics is determined by thermal activation over energy barriers. The barrier to overturning of the spins in a domain of size $L$ is proportional to $Z\mathrm{ln}L$, where $Z$ is a new geometrical parameter characterizing the fractal. A new "singular" dynamic scaling is found in which the effective dynamic critical exponent diverges at criticality.