Critical behavior of charge-density waves below threshold: Numerical and scaling analysis

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Abstract
The critical behavior of pinned charge-density waves (CDW’s) is studied as the threshold for sliding is approached. Using the Fukuyama-Lee-Rice Hamiltonian with relaxational dynamics, the polarization and linear response are calculated numerically. Analytic bounds on the subthreshold motion are used to develop fast numerical algorithms for evolving the CDW configuration. Two approaches to threshold, ‘‘reversible’’ and ‘‘irreversible,’’ are studied, which differ in the details of the critical behavior. On the irreversible approach to threshold, the response due to avalanches triggered by local instabilities dominates the polarizability, which diverges in one and two dimensions. Such ‘‘jumps’’ are absent on the reversible approach. On both the reversible and irreversible approach in two dimensions, the linear response, which does not include the jumps, is singular, but does not diverge. Characteristic diverging length scales are studied using finite-size scaling of the sample-to-sample variations of the threshold field in finite systems and finite-size effects in the linear polarizability and the irreversible polarization. A dominant diverging correlation length is found which controls the threshold field distribution, finite-size effects in the irreversible polarization, and a cutoff size for the avalanche size distribution. This length diverges with an exponent ν≊2.0,1.0 in dimensions d=1,2, respectively. A distinct exponent describes the finite-size effects for the linear polarizability in single samples. Our results are compared with those for related models and questions are raised concerning the relationship of the static critical behavior below threshold to the dynamic critical behavior in the sliding state above threshold.