title: Extremal statistics in the energetics of domain walls.
abstract: We study at T=0 the minimum energy of a domain wall and its gap to the first excited state, concentrating on two-dimensional random-bond Ising magnets. The average gap scales as deltaE1 approximately L(straight theta)f(N(z)), where f(y) approximately [ln y](-1/2), straight theta is the energy fluctuation exponent, L is the length scale, and N(z) is the number of energy valleys. The logarithmic scaling is due to extremal statistics, which is illustrated by mapping the problem into the Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of domain walls also has a logarithmic dependence on the system size.
authors: Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland.
authors: E T
authors: ET
authors: Seppälä
authors: M J
authors: MJ
authors: Alava
authors: P M
authors: PM
authors: Duxbury