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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Disordered elastic systems exhibit complex behavior when driven.
  • Pinning forces on the center of mass fluctuate, characterized by mean and variance.
  • Two well-understood fixed points exist: the depinning and zero-temperature equilibrium fixed points.

Purpose of the Study:

  • To numerically quantify the crossover between the depinning and zero-temperature equilibrium fixed points.
  • To explore the parameter space of driving velocity (v > 0) and temperature (T > 0).

Main Methods:

  • Utilized the functional renormalization group in the limit of vanishing temperature (T→0) and vanishing driving velocity (v→0).
  • Employed numerical methods to analyze the crossover in the T>0 and v>0 parameter space.

Main Results:

  • Characterized fluctuating pinning forces with mean f_{c}=-F_{w}[over ¯] and variance Δ(w)=F_{w}F_{0}[over ¯]^{c}.
  • Identified and analyzed deformations around the depinning and zero-temperature equilibrium fixed points.

Conclusions:

  • The study provides a numerical quantification of the crossover between distinct critical behaviors in disordered elastic systems.
  • Understanding this crossover is crucial for predicting system dynamics across various temperature and driving velocity regimes.