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Related Experiment Videos

Exact multilocal renormalization group and applications to disordered problems.

P Chauve1, P Le Doussal

  • 1Laboratoire de Physique des Solides, Université Paris-Sud, Bâtiment 510, 91405 Orsay, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
Summary

We introduce the exact multilocal renormalization group (EMRG) to precisely analyze complex physical theories. This controlled method accurately models phenomena like disordered elastic systems and domain wall behavior.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Statistical Mechanics

Background:

  • The exact renormalization group (ERG) provides a powerful framework for studying systems across various scales.
  • Existing projection methods like derivative expansions can lack control and accuracy.
  • Functional renormalization group (FRG) approaches often rely on hard cutoff schemes.

Purpose of the Study:

  • To develop a novel, controlled method, the exact multilocal renormalization group (EMRG), applicable to a wide range of theories.
  • To improve the analysis of complex systems, including disordered elastic systems and domain walls.
  • To provide an exact renormalization group (RG) framework that overcomes limitations of existing projection methods.

Main Methods:

  • Systematic multilocal expansion of the Polchinski-Wilson exact renormalization group (ERG) equation.

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  • Development of a scheme to compute correlation functions by integrating out nonlocal interactions.
  • Reduction of the ERG equation to a flow equation for the local part of the interaction functional, exact to any given order.
  • Perturbative analysis around fixed points.

    • Main Results:

    • The EMRG method is demonstrated to be controlled and applicable to broad theories, unlike projection methods.
    • Universality is verified to O(epsilon=4-D) for T=0 FRG equations and correlations.
    • Finite temperature extension yields universal finite size susceptibility fluctuations characterizing mesoscopic behavior.
    • A universal scaling function is obtained to O(epsilon(1/3)) for domain wall ground states in random fields.

    Conclusions:

    • The EMRG method offers a precise and controlled approach for renormalization group studies.
    • It provides significant advantages over traditional projection methods and hard cutoff FRG schemes.
    • The method successfully describes complex phenomena in condensed matter and statistical physics, including universality and mesoscopic behavior.