Extremal statistics in the energetics of domain walls - art. no. 066110

We study at T=0 the minimum energy of a domain wall and its gap to the firs t excited state, concentrating on two-dimensional random-bond Ising magnets . The average gap scales as DeltaE(1)similar toL(theta)f(N-z), where f(y) s imilar to [ln y](- 1/2), theta is the energy fluctuation exponent, L is the length scale, and N-z is the number of energy valleys. The logarithmic sca ling is due to extremal statistics, which is illustrated by mapping the pro blem into the Kardar-Parisi-Zhang roughening process. It follows that the s usceptibility of domain walls also has a logarithmic dependence on the syst em size.