Numerical studies of the 2 and 3D gauge glass at low temperature

We report results from Monte Carlo simulations of the two- and three-dimensional gauge glass at low temperature using parallel tempering Monte Carlo. In two dimensions, we find strong evidence for a zero-temperature transition. By means of finite-size scaling, we determine the stiffness exponent theta = -0.39 +/- 0.03. In three dimensions, where a finite-temperature transition is well established, we find theta = 0.27 +/- 0.01, compatible with recent results from domain-wall renormalization group studies.Comment: 3 pages, 3 figures. Proceedings of "2002 MMM Conference", Tampa, F

Ordering of the three-dimensional Heisenberg spin glass in magnetic fields

Spin and chirality orderings of the three-dimensional Heisenberg spin glass are studied under magnetic fields in light of the recently developed spin-chirality decoupling-recoupling scenario. It is found by Monte Carlo simulations that the chiral-glass transition and the chiral-glass ordered state, which are essentially of the same character as their zero-field counterparts, occur under magnetic fields. Implication to experimental phase diagram is discussed.Comment: 5 pages, 3 figure

The Lower Critical Dimension of the XY Spin Glass

We investigate the XY spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to L=12 (2D) and L=8 (3D) strongly suggest that the lower critical dimension for spin-glass ordering may be $d_{c}\approx 3$ rather than four as is commonly believed. Our 3D data favor the scenario of a low but finite spin-glass ordering temperature below the chiral transition but they are also compatible with the system being at or slightly below its lower critical dimension.Comment: 4 pages, 3 ps figures. Typos have been corrected, one reference has been added and the concluding paragraph has been expanded. To appear in Phys. Rev. Let

Numerical Study of Spin and Chiral Order in a Two-Dimensional XY Spin Glass

The two dimensional XY spin glass is studied numerically by a finite size scaling method at T=0 in the vortex representation which allows us to compute the exact (in principle) spin and chiral domain wall energies. We confirm earlier predictions that there is no glass phase at any finite T. Our results strongly support the conjecture that both spin and chiral order have the same correlation length exponent $\nu \approx 2.70$. We obtain preliminary results in 3d.Comment: 4 pages, 2 figures, revte

Application of a minimum cost flow algorithm to the three-dimensional gauge glass model with screening

We study the three-dimensional gauge glass model in the limit of strong screening by using a minimum cost flow algorithm, enabling us to obtain EXACT ground states for systems of linear size L<=48. By calculating the domain-wall energy, we obtain the stiffness exponent theta = -0.95+/-0.03, indicating the absence of a finite temperature phase transition, and the thermal exponent nu=1.05+/-0.03. We discuss the sensitivity of the ground state with respect to small perturbations of the disorder and determine the overlap length, which is characterized by the chaos exponent zeta=3.9+/-0.2, implying strong chaos.Comment: 4 pages RevTeX, 2 eps-figures include

Numerical study of the strongly screened vortex glass model in an external field

The vortex glass model for a disordered high-T_c superconductor in an external magnetic field is studied in the strong screening limit. With exact ground state (i.e. T=0) calculations we show that 1) the ground state of the vortex configuration varies drastically with infinitesimal variations of the strength of the external field, 2) the minimum energy of global excitation loops of length scale L do not depend on the strength of the external field, however 3) the excitation loops themself depend sensibly on the field. From 2) we infer the absence of a true superconducting state at any finite temperature independent of the external field.Comment: 6 pages RevTeX, 5 eps-figures include

Phase Transitions in the Two-Dimensional XY Model with Random Phases: a Monte Carlo Study

We study the two-dimensional XY model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and temperature. If the strength of the randomness is less than a critical value, $\sigma_{c}$, the system has a Kosterlitz-Thouless (KT) phase transition from the paramagnetic phase to a state with quasi-long-range order. Our data suggest that the latter exists down to T=0 in contradiction with theories that predict the appearance of a low-temperature reentrant phase. At the critical disorder $T_{KT}\rightarrow 0$ and for $\sigma > \sigma_{c}$ there is no quasi-ordered phase. At zero temperature there is a phase transition between two different glassy states at $\sigma_{c}$. The functional dependence of the correlation length on $\sigma$ suggests that this transition corresponds to the disorder-driven unbinding of vortex pairs.Comment: LaTex file and 18 figure

Numerical Study of Order in a Gauge Glass Model

The XY model with quenched random phase shifts is studied by a T=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 $\theta$. This method gives $\theta = -0.36\pm0.013$ in 2d and $\theta = +0.31\pm 0.015$ in 3d, which are considerably larger than previous estimates, strongly suggesting that the lower critical dimension is less than three. Some arguments in favor of these new estimates are given.Comment: 4 pages, 2 figures, revtex. Submitted to Phys. Rev. Let