Zero-temperature glass transition in the two-dimensional gauge glass model

Abstract

We investigate dynamic scaling properties of the two-dimensional gauge glass model for the vortex glass phase in superconductors with quenched disorder. From extensive Monte Carlo simulations we obtain static and dynamic finite-size scaling behavior, where the static simulations use a temperature exchange method to ensure convergence at low temperatures. Both static and dynamic scaling of Monte Carlo data is consistent with a glass transition at zero temperature, with correlation length exponent given by $1/\ensuremath{\nu}=0.36\ifmmode\pm\else\textpm\fi{}0.03.$ We study a dynamic correlation function for the superconducting order parameter, as well as the phase slip resistance. From the scaling of these two functions, we find evidence for two distinct diverging correlation times at the zero-temperature glass transition. The longer of these time scales is associated with phase slip fluctuations across the system that lead to finite resistance at any finite temperature. The shorter time scale can be described by the form $\ensuremath{\tau}\ensuremath{\sim}{\ensuremath{\xi}}^{z},$ with a dynamic exponent $z=2.7\ifmmode\pm\else\textpm\fi{}0.2,$ and corresponds to local phase fluctuations.