Superconductor-to-Normal Phase Transition in a Vortex Glass Model: Numerical Evidence for a New Percolation Universality Class

The three-dimensional strongly screened vortex-glass model is studied numerically using methods from combinatorial optimization. We focus on the effect of disorder strength on the ground state and found the existence of a disorder-driven normal-to-superconducting phase transition. The transition turns out to be a geometrical phase transition with percolating vortex loops in the ground state configuration. We determine the critical exponents and provide evidence for a new universality class of correlated percolation.Comment: 11 pages LaTeX using IOPART.cls, 11 eps-figures include

Dislocations in the ground state of the solid-on-solid model on a disordered substrate

We investigate the effects of topological defects (dislocations) to the ground state of the solid-on-solid (SOS) model on a simple cubic disordered substrate utilizing the min-cost-flow algorithm from combinatorial optimization. The dislocations are found to destabilize and destroy the elastic phase, particularly when the defects are placed only in partially optimized positions. For multi defect pairs their density decreases exponentially with the vortex core energy. Their mean distance has a maximum depending on the vortex core energy and system size, which gives a fractal dimension of $1.27 \pm 0.02$. The maximal mean distances correspond to special vortex core energies for which the scaling behavior of the density of dislocations change from a pure exponential decay to a stretched one. Furthermore, an extra introduced vortex pair is screened due to the disorder-induced defects and its energy is linear in the vortex core energy.Comment: 6 pages RevTeX, eps figures include

Fluctuation Dissipation Ratio in Three-Dimensional Spin Glasses

We present an analysis of the data on aging in the three-dimensional Edwards Anderson spin glass model with nearest neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean field theory. We measure the parameter $x(q)$ describing the violation of the relation among correlation and response function implied by the fluctuation dissipation theorem.Comment: LaTeX 10 pages + 4 figures (appended as uuencoded compressed tar-file), THP81-9

Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions

We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confronted with numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L<=512) are found to follow conformal predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution show multi-scaling character. In the Griffiths phase, which is an extended part of the off-critical region average autocorrelations have a power-law form with a non-universal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.Comment: 19 pages RevTeX, eps-figures include

Dynamical simulation of spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses

Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied with and without randaom magnetic anisotropy by dynamical Monte Carlo simulations. In isotropic case, clear evidence of a finite-temperature chiral-glass transition is presented. While the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminisecnt of the one observed in the mean-field model. In anisotropic case, asymptotic mixing of the spin and the chirality is observed in the off-equilibrium dynamics.Comment: 4 pages including 5 figures, LaTex, to appear in Phys. Rev. Let

Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models

The low temperature dynamics of the two- and three-dimensional Ising spin glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the autocorrelation function $C(t,t_w)=[]_{av}$ a typical aging scenario with a $t/t_w$ scaling is established. Investigating spatial correlations we find an algebraic growth law $\xi(t_w)\sim t_w^{\alpha(T)}$ of the average domain size. The spatial correlation function $G(r,t_w)=[< S_i(t_w)S_{i+r}(t_w)>^2]_{av}$ scales with $r/\xi(t_w)$. The sensitivity of the correlations in the spin glass phase with respect to temperature changes is examined by calculating a time dependent overlap length. In the two dimensional model we examine domain growth with a new method: First we determine the exact ground states of the various samples (of system sizes up to $100\times 100$) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation.Comment: 38 pages, RevTeX, 14 postscript figure

Dynamic Scaling in Diluted Systems Phase Transitions: Deactivation trough Thermal Dilution

Activated scaling is confirmed to hold in transverse field induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold but well bellow and above it including the Griffiths-McCoy phase. A novel deactivation phenomena in the Griffiths-McCoy phase is observed using a thermal (in contrast to random) dilution of the system.Comment: 4 pages, 4 figures, RevTe

Small catchment runoff sensitivity to station density and spatial interpolation: Hydrological modeling of heavy rainfall using a dense rain Gauge network

Precipitation is the most important input to hydrological models, and its spatial variability can strongly influence modeled runoff. The highly dense station network WegenerNet (0.5 stations per km2) in southeastern Austria offers the opportunity to study the sensitivity of modeled runoff to precipitation input. We performed a large set of runoff simulations (WaSiM model) using 16 subnetworks with varying station densities and two interpolation schemes (inverse distance weighting, Thiessen polygons). Six representative heavy precipitation events were analyzed, placing a focus on small subcatchments (10–30 km2) and different event durations. We found that the modeling performance generally improved when the station density was increased up to a certain resolution: a mean nearest neighbor distance of around 6 km for long-duration events and about 2.5 km for short-duration events. However, this is not always true for small subcatchments. The sufficient station density is clearly dependent on the catchment area, event type, and station distribution. When the network is very dense (mean distance &lt; 1.7 km), any reasonable interpolation choice is suitable. Overall, the station density is much more important than the interpolation scheme. Our findings highlight the need to study extreme precipitation characteristics in combination with runoff modeling to decompose precipitation uncertainties more comprehensively

Impact of Interdisciplinary Undergraduate Research in Mathematics and Biology on the Development of a New Course Integrating Five STEM Disciplines

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a course for first-year students that integrates the material in the first course of the major in each of biology, chemistry, mathematics, computer science, and physics

Critical properties of loop percolation models with optimization constraints

We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional bond percolation. In contrast to this an optimization constraint for the loop configurations, which then have to minimize a particular generic energy function, leads to a percolation transition that constitutes a new universality class, for which we report the critical exponents. Implication for the physics of solid-on-solid and vortex glass models are discussed.Comment: 8 pages, 8 figure