%0 Journal Article
%T Extremal statistics in the energetics of domain walls
%A E. T. Sepp£¿l£¿
%A M. J. Alava
%A P. M. Duxbury
%J Physics
%D 2001
%I arXiv
%R 10.1103/PhysRevE.63.066110
%X 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 $\Delta E_1 \sim L^\theta f(N_z)$, where $f(y) \sim [\ln y]^{-1/2}$, $\theta$ is the energy fluctuation exponent, $L$ length scale, and $N_z$ 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 has also a logarithmic dependence on system size.
%U http://arxiv.org/abs/cond-mat/0102318v1