Extremal statistics in the energetics of domain walls

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

doi:10.1103/PhysRevE.63.066110

Extremal statistics in the energetics of domain walls

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

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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 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 language	English
Article number	066110
Pages (from-to)	1-4
Journal	Physical Review E
Volume	63
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevE.63.066110
Publication status	Published - 2001
MoE publication type	A1 Journal article-refereed

Keywords

Interface and surface thermodynamics
Interface structure and roughness
random magnets

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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 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.",

keywords = "Interface and surface thermodynamics, Interface structure and roughness, random magnets, Interface and surface thermodynamics, Interface structure and roughness, random magnets, Interface and surface thermodynamics, Interface structure and roughness, random magnets",

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AU - Alava, M.J.

AU - Duxbury, P.M.

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Y1 - 2001

N2 - 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.

AB - 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.

KW - Interface and surface thermodynamics

KW - Interface structure and roughness

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KW - Interface structure and roughness

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KW - Interface and surface thermodynamics

KW - Interface structure and roughness

KW - random magnets

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