Pinning and Roughening of Domain Walls in Ising Systems Due to Random Impurities

Randomly placed impurities that alter the local exchange couplings, but do not generate random fields or destroy the long-range order, roughen domain walls in Ising systems for dimensionality $\frac{5}{3}<d<\mathrm{}5\mathrm{}$. They also pin (localize) the walls in energetically favorable positions. This drastically slows down the kinetics of ordering. The pinned domain wall is a new critical phenomenon governed by a zero-temperature fixed point. For $d=2\mathrm{}$, the critical exponents for domain-wall pinning energies and roughness as a function of length scale are estimated from numerically generated ground states.