Effect of disorder and lattice type on domain-wall motion in two dimensions

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Abstract
We study the general problem of interface motion through a disordered medium taking as an example the random-field Ising model in two dimensions. Spins are placed on the sites of a square, triangular, or honeycomb array. Each interacts with a random local field from a bounded distribution. Growth of a domain through the array is driven by a uniform external magnetic field. When the random field strength is large, the domain of flipped spins forms a fractal percolationlike pattern. As the randomness decreases, there is a transition to compact two-dimensional growth with a faceted interface. In the square and triangular lattices there is a power-law divergence of a characteristic correlation length or fingerwidth at the transition. The exponents relating this divergence to the probabilities that local spin configurations are stable are found to be universal. In contrast, there is a discontinuous transition from fractal to faceted growth on the honeycomb lattice that occurs in the limit of zero randomness. We show that the problem of domain growth is related to a continuous family of bootstrap percolation models.