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Related Experiment Videos

Universal energy distribution for interfaces in a random-field environment.

Andrei A Fedorenko1, Semjon Stepanow

  • 1Martin-Luther-Universität Halle, Fachbereich Physik, D-06099 Halle, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
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We analyzed interface energy distributions in random fields. For one-dimensional systems, energy scales with length (L) and approaches extreme value statistics for large interfaces.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Disordered Systems

Background:

  • Understanding the behavior of interfaces in disordered systems is crucial for materials science and statistical physics.
  • The energy distribution function provides insights into the stability and properties of these interfaces.

Purpose of the Study:

  • To investigate the energy distribution function (rho(E)) for interfaces in a random-field environment at zero temperature.
  • To analyze the impact of disorder strength on the energy distribution using both perturbative and non-perturbative methods.

Main Methods:

  • Summing leading terms in the perturbation expansion of rho(E) in powers of disorder strength.
  • Employing the functional renormalization group to account for non-perturbative disorder effects.

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Main Results:

  • For a one-dimensional interface of length L, the average energy scales as (R) proportional to L ln L.
  • The variance of the energy scales as DeltaE(R) proportional to L.
  • The energy distribution function converges to the Gumbel distribution for large L, indicating extreme value statistics.

Conclusions:

  • The study provides a detailed characterization of interface energy distributions in random-field environments.
  • The findings highlight the transition to extreme value statistics for large one-dimensional interfaces under disorder.
  • The methods employed offer a robust framework for studying similar systems in condensed matter physics.