Avalanches and the Renormalization Group for Pinned Charge-Density Waves

TL;DR

This paper investigates the critical behavior of pinned charge-density waves near the threshold field, using renormalization group techniques and automaton models, revealing universal avalanche phenomena and diverging correlation lengths.

Contribution

It applies renormalization group analysis to pinned CDWs and automaton models, showing their critical behavior and avalanche dynamics near the threshold.

Findings

Renormalization group captures divergences in polarization and correlation length.

Automaton models exhibit the same critical behavior and avalanche scaling.

Numerical results agree with analytical predictions in 2D and 3D.

Abstract

The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization group treatment can be used successfully to find the divergences in the polarization and the correlation length, and, to first order in an $\epsilon = 4-d$ expansion, the diverging time scale. The automaton models studied are a charge-density wave model and a ``sandpile'' model with periodic boundary conditions; these models are found to have the same critical behavior, associated with diverging avalanche sizes. The numerical results for the polarization and the diverging length and time scales in dimensions $d=2,3$ are in agreement with the analytical treatment. These results clarify the connections between the behaviour above and below threshold: the characteristic correlation lengths on both sides of the transition diverge with different exponents. The scaling of the distribution of avalanches on the approach to threshold is found to be different for automaton and continuous-variable models.