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

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

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

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

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

Quantum vs. Geometric Disorder in a Two-Dimensional Heisenberg Antiferromagnet

We present a numerical study of the spin-1/2 bilayer Heisenberg antiferromagnet with random interlayer dimer dilution. From the temperature dependence of the uniform susceptibility and a scaling analysis of the spin correlation length we deduce the ground state phase diagram as a function of nonmagnetic impurity concentration p and bilayer coupling g. At the site percolation threshold, there exists a multicritical point at small but nonzero bilayer coupling g_m = 0.15(3). The magnetic properties of the single-layer material La_2Cu_{1-p}(Zn,Mg)_pO_4 near the percolation threshold appear to be controlled by the proximity to this new quantum critical point.Comment: minor changes, updated figure

Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential

We study a lattice model of a three-dimensional periodic elastic medium at zero temperature with exact combinatorial optimization methods. A competition between pinning of the elastic medium, representing magnetic flux lines in the mixed phase of a superconductor or charge density waves in a crystal, by randomly distributed impurities and a periodic lattice potential gives rise to a continuous phase transition from a flat phase to a rough phase. We determine the critical exponents of this roughening transition via finite size scaling obtaining $\nu\approx1.3$, $\beta\approx0.05$, $\gamma/\nu\approx2.9$ and find that they are universal with respect to the periodicity of the lattice potential. The small order parameter exponent is reminiscent of the random field Ising critical behavior in 3$d$.Comment: 4 pages, 3 eps-figures include