Evidence of Two Distinct Dynamic Critical Exponents in Connection with Vortex Physics

The dynamic critical exponent $z$ is determined from numerical simulations for the three-dimensional (3D) lattice Coulomb gas (LCG) and the 3D XY models with relaxational dynamics. It is suggested that the dynamics is characterized by two distinct dynamic critical indices $z_0$ and $z$ related to the divergence of the relaxation time $tau$ by $taupropto xi^{z_0}$ and $taupropto k^{-z}$, where $xi$ is the correlation length and $k$ the wavevector. The values determined are $z_0approx 1.5$ and $zapprox 1$ for the 3D LCG and $z_0approx 1.5$ and $zapprox 2$ for the 3D XY model. It is argued that the nonlinear $IV$ exponent relates to $z_0$, whereas the usual Hohenberg-Halperin classification relates to $z$. Possible implications for the interpretation of experiments are pointed out. Comparisons with other existing results are discussed.