Numerical Study of Order in a Gauge Glass Model

Abstract

The $\mathrm{XY}$ model with quenched random phase shifts is studied by a $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ finite size defect energy scaling method in 2D and 3D. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state configuration for a given realization of disorder. A numerical technique, which is exact in principle, is used to evaluate this energy and to estimate the stiffness exponent $\ensuremath{\theta}$. This method gives $\ensuremath{\theta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}0.36\ifmmode\pm\else\textpm\fi{}0.01$ in 2D and $\ensuremath{\theta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}+0.31\ifmmode\pm\else\textpm\fi{}0.015$ in 3D, which are considerably larger than previous estimates, strongly suggesting that the lower critical dimension is less than 3. Some arguments in favor of these new estimates are given.