Extremal statistics in the energetics of domain walls

Eira T. Seppälä, M.J. Alava, P.M. Duxbury

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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 ΔE1∼Lθf(Nz), where f(y)∼[lny]−1/2, θ is the energy fluctuation exponent, L is the length scale, and Nz 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.
Original languageEnglish
Article number066110
Pages (from-to)1-4
JournalPhysical Review E
Issue number6
Publication statusPublished - 2001
MoE publication typeA1 Journal article-refereed


  • Interface and surface thermodynamics
  • Interface structure and roughness
  • random magnets


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