Temperature-disorder phase diagram of a three-dimensional gauge-glass model

We investigate the temperature-disorder (T-sigma) phase diagram of a three-dimensional gauge glass model, which is a cubic-lattice nearest-neighbor XY model with quenched random phase shifts A(xy) at the bonds. We consider the uncorrelated phase-shift distribution P(A(xy)) similar to exp[(cosA(xy))/sigma], which has the pure XY model, and the uniform distribution of random phase shifts as extreme cases at sigma = 0 and sigma -> infinity, respectively, and which gives rise to equal magnetic and overlap correlation functions when T = s. Our study is mostly based on numerical Monte Carlo simulations. While the high-temperature phase is always paramagnetic, at low temperatures there is a ferromagnetic phase for weak disorder (small sigma) and a glassy phase at large disorder (large sigma). These three phases are separated by transition lines with different magnetic and glassy critical behaviors. The disorder induced by the random phase shifts turns out to be irrelevant at the paramagnetic-ferromagnetic transition line, where the critical behavior belongs to the 3D XY universality class of pure systems; disorder gives rise only to very slowly decaying scaling corrections. The glassy critical behavior along the paramagnetic-glassy transition line belongs to the gauge-glass universality class, with a quite large exponent. = 3.2(4). These transition lines meet at a multicritical point M, located at T-M = sigma(M) = 0.7840(2). The low-temperature ferromagnetic and glassy phases are separated by a third transition line, from M down to the T = 0 axis, which is slightly reentrant.