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Measuring functional renormalization group fixed-point functions for pinned manifolds.

A Alan Middleton1, Pierre Le Doussal, Kay Jörg Wiese

  • 1Department of Physics, Syracuse University, Syracuse, New York 13244, USA.

Physical Review Letters
|May 16, 2007
PubMed
Summary
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This study numerically tests functional renormalization group analysis for interfaces in disordered systems. Results confirm a linear cusp in the disorder correlator R(u) across various dimensions and disorder types.

Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Computational physics

Background:

  • Interfaces in disordered systems are crucial in materials science.
  • Functional renormalization group (FRG) is a powerful theoretical tool.
  • Understanding quenched disorder effects on interfaces is challenging.

Purpose of the Study:

  • To numerically test the accuracy of functional renormalization group (FRG) analysis for interfaces pinned by quenched disorder.
  • To compute the fixed-point function R(u), the correlator of the coarse-grained disorder.
  • To investigate deviations from theoretical predictions and explore higher-order corrections.

Main Methods:

  • Exact numerical minimization of interface energies.
  • Computation of the fixed-point function R(u).

Related Experiment Videos

  • Analysis of disorder correlators in various dimensions (D=d+1).

    • Main Results:

    • Confirmed a linear cusp in R''(u) for random bond, random field, and periodic disorders in dimensions d=1, 2, 3.
    • Observed functional shocks leading to the cusp.
    • Identified small but significant deviations from 1-loop calculations, compared with 2-loop corrections.

    Conclusions:

    • Numerical results validate FRG analysis for disordered interfaces.
    • The study provides insights into the nature of functional shocks and cusp formation.
    • Highlights the importance of higher-order corrections in FRG for disordered systems.