Extremal statistics in the energetics of domain walls

Details Extremal statistics in the energetics of domain walls Extremal statistics in the energetics of domain walls

2001-02-18

arxiv.org/abs/cond-mat/0102318v1

Phys. Rev. E 63, 066110 (2001)

Physics

Condensed Matter

Statistical Mechanics

Accepted for publication in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.63.066110

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.

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