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 $\Delta E_1\sim L^{\theta }f(N_z)$, 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.

Accepted for publication in Phys. Rev. E

Cited by in corpus (5)

• Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids
• Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model
• Directed polymers and interfaces in random media : free-energy optimization via confinement in a wandering tube
• On the critical exponent $\alpha$ of the 5D random-field Ising model
• Elastic manifolds in disordered environments: energy statistics