Ground state of the random-bond spin-1 Heisenberg chain

Stochastic series expansion quantum Monte Carlo is used to study the ground state of the antiferromagnetic spin-1 Heisenberg chain with bond disorder. Typical spin- and string-correlations functions behave in accordance with real-space renormalization group predictions for the random-singlet phase. The average string-correlation function decays algebraically with an exponent of -0.378(6), in very good agreement with the prediction of $-(3-\sqrt{5})/2\simeq -0.382$, while the average spin-correlation function is found to decay with an exponent of about -1, quite different from the expected value of -2. By implementing the concept of directed loops for the spin-1 chain we show that autocorrelation times can be reduced by up to two orders of magnitude.Comment: 9 pages, 10 figure

Numerical studies of the two- and three-dimensional gauge glass at low temperature

We present results from Monte Carlo simulations of the two- and three-dimensional gauge glass at low temperature using the parallel tempering Monte Carlo method. Our results in two dimensions strongly support the transition being at T_c=0. A finite-size scaling analysis, which works well only for the larger sizes and lower temperatures, gives the stiffness exponent theta = -0.39 +/- 0.03. In three dimensions we find theta = 0.27 +/- 0.01, compatible with recent results from domain wall renormalization group studies.Comment: 7 pages, 10 figures, submitted to PR

Spin Reduction Transition in Spin-3/2 Random Heisenberg Chains

Random spin-3/2 antiferromagnetic Heisenberg chains are investigated using an asymptotically exact renormalization group. Randomness is found to induce a quantum phase transition between two random-singlet phases. In the strong randomness phase the effective spins at low energies are S_eff=3/2, while in the weak randomness phase the effective spins are S_eff=1/2. Separating them is a quantum critical point near which there is a non-trivial mixture of S=1/2, S=1, and S=3/2 effective spins at low temperatures.Comment: 4 pages, 3 figures. Typos correcte

Zero Temperature Glass Transition in the Two-Dimensional Gauge Glass Model

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. 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, while the shorter time scale is associated with local phase fluctuations.Comment: 8 pages, 10 figures; v2: some minor correction

On the existence of a finite-temperature transition in the two-dimensional gauge glass

Results from Monte Carlo simulations of the two-dimensional gauge glass supporting a zero-temperature transition are presented. A finite-size scaling analysis of the correlation length shows that the system does not exhibit spin-glass order at finite temperatures. These results are compared to earlier claims of a finite-temperature transition.Comment: 4 pages, 2 figure

Spin-3/2 random quantum antiferromagnetic chains

We use a modified perturbative renormalization group approach to study the random quantum antiferromagnetic spin-3/2 chain. We find that in the case of rectangular distributions there is a quantum Griffiths phase and we obtain the dynamical critical exponent $Z$ as a function of disorder. Only in the case of extreme disorder, characterized by a power law distribution of exchange couplings, we find evidence that a random singlet phase could be reached. We discuss the differences between our results and those obtained by other approaches.Comment: 4 page

Magnetic Reversal on Vicinal Surfaces

We present a theoretical study of in-plane magnetization reversal for vicinal ultrathin films using a one-dimensional micromagnetic model with nearest-neighbor exchange, four-fold anisotropy at all sites, and two-fold anisotropy at step edges. A detailed "phase diagram" is presented that catalogs the possible shapes of hysteresis loops and reversal mechanisms as a function of step anisotropy strength and vicinal terrace length. The steps generically nucleate magnetization reversal and pin the motion of domain walls. No sharp transition separates the cases of reversal by coherent rotation and reversal by depinning of a ninety degree domain wall from the steps. Comparison to experiment is made when appropriate.Comment: 12 pages, 8 figure

Percolation in random environment

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are non-universal, whereas for strong enough disorder the system scales into an {\it infinite randomness fixed point} in which the critical exponents are exactly known.Comment: 8 pages, 7 figure

Frustrated two-dimensional Josephson junction array near incommensurability

To study the properties of frustrated two-dimensional Josephson junction arrays near incommensurability, we examine the current-voltage characteristics of a square proximity-coupled Josephson junction array at a sequence of frustrations f=3/8, 8/21, 0.382 $(\approx (3-\sqrt{5})/2)$, 2/5, and 5/12. Detailed scaling analyses of the current-voltage characteristics reveal approximately universal scaling behaviors for f=3/8, 8/21, 0.382, and 2/5. The approximately universal scaling behaviors and high superconducting transition temperatures indicate that both the nature of the superconducting transition and the vortex configuration near the transition at the high-order rational frustrations f=3/8, 8/21, and 0.382 are similar to those at the nearby simple frustration f=2/5. This finding suggests that the behaviors of Josephson junction arrays in the wide range of frustrations might be understood from those of a few simple rational frustrations.Comment: RevTex4, 4 pages, 4 eps figures, to appear in Phys. Rev.

Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder systems: One-Particle Properties and Boundary Effects

Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\epsilon$, the single-particle Green function decays in real space like $G(x,\epsilon) \propto (1/x)^{3/2}$. It follows that at these energies the correlations in the disordered system are strong -- even stronger than in the pure system without the gap. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as $1/\sqrt{x}$ and the density of states saturates to its bulk value on the scale $L_\epsilon \propto \ln^2 (1/\epsilon)$. This scale is different from the Thouless localization length $\lambda_\epsilon\propto\ln (1/\epsilon)$. We also discuss some implications of these results for the spin systems and their relation to the investigations based on real-space renormalization group approach.Comment: 26 pages, LaTex, 9 PS figures include