Critical behavior of sliding charge-density waves in 4-ε dimensions

Abstract

The critical dynamics of charge-density waves (CDW's) just above the threshold for steady-state sliding motion are studied via a renormalization-group expansion in 4-\ensuremath{\epsilon} dimensions. This necessitates the simultaneous treatment of the long-wavelength low-frequency dynamics as well as the singular behavior associated with the jumps of local regions during which the local velocities become large. Scaling forms are obtained for response and correlation functions in the critical region, and exponent identities are derived. To leading order in \ensuremath{\epsilon}, the exponent \ensuremath{\zeta} of the CDW current ${\mathit{I}}_{\mathrm{CDW}}$\ensuremath{\sim}(V-${\mathit{V}}_{\mathit{T}}$${)}^{\mathrm{\ensuremath{\zeta}}}$ just above the threshold voltage ${\mathit{V}}_{\mathit{T}}$ is found to be \ensuremath{\zeta}=1-\ensuremath{\epsilon}/6+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$), in reasonable agreement with recent numerical simulations in two and three dimensions. The spatial correlations in the local velocities of the CDW decay exponentially with a correlation length, which diverges with an exponent \ensuremath{\nu} exactly equal to 1/2. Nevertheless, finite-size scaling of many quantities will be determined by a different exponent ${\ensuremath{\nu}}_{\mathrm{FS}}$=1/2+\ensuremath{\epsilon}/8+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$)=2/d+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$). The other exponents are related to \ensuremath{\zeta}, \ensuremath{\nu}, and ${\ensuremath{\nu}}_{\mathrm{FS}}$. Simple forms of long-wavelength low-frequency correlation and response functions in the moving phase are obtained to all orders in perturbation theory.