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 $\mathrm{XY}$ 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 $\tau \propto {\xi }^{z_0}$ and $\tau \propto k^{-z}$, where $\xi$ is the correlation length and $k$ the wave vector. The values determined are $z_0\approx 1.5$ and $z\approx 1$ for the 3D LCG and $z_0\approx 1.5$ and $z\approx 2$ for the 3D $\mathrm{XY}$ model. Comparisons with other results are discussed.