Fractal Droplets in Two Dimensional Spin Glasses

The two-dimensional Edwards-Anderson model with Gaussian bond distribution is investigated at T=0 with a numerical method. Droplet excitations are directly observed. It turns out that the averaged volume of droplets is proportional to l^D with D = 1.80(2) where l is the spanning length of droplets, revealing their fractal nature. The exponent characterizing the l dependence of the droplet excitation energy is estimated to be -0.42(4), clearly different from the stiffness exponent for domain wall excitations.Comment: 4 pages 4 figure

Quantum Effects and Broken Symmetries in Frustrated Antiferromagnets

We investigate the interplay between frustration and zero-point quantum fluctuations in the ground state of the triangular and $J_1{-}J_2$ Heisenberg antiferromagnets, using finite-size spin-wave theory, exact diagonalization, and quantum Monte Carlo methods. In the triangular Heisenberg antiferromagnet, by performing a systematic size-scaling analysis, we have obtained strong evidences for a gapless spectrum and a finite value of the thermodynamic order parameter, thus confirming the existence of long-range N\'eel order.The good agreement between the finite-size spin-wave results and the exact and quantum Monte Carlo data also supports the reliability of the spin-wave expansion to describe both the ground state and the low-energy spin excitations of the triangular Heisenberg antiferromagnet. In the $J_1{-}J_2$ Heisenberg model, our results indicate the opening of a finite gap in the thermodynamic excitation spectrum at $J_2/J_1 \simeq 0.4$, marking the melting of the antiferromagnetic N\'eel order and the onset of a non-magnetic ground state. In order to characterize the nature of the latter quantum-disordered phase we have computed the susceptibilities for the most important crystal symmetry breaking operators. In the ordered phase the effectiveness of the spin-wave theory in reproducing the low-energy excitation spectrum suggests that the uniform spin susceptibility of the model is very close to the linear spin-wave prediction.Comment: Review article, 44 pages, 18 figures. See also PRL 87, 097201 (2001

In-flight transition measurement on a 10 deg cone at Mach numbers from 0.5 to 2.0

Boundary layer transition measurements were made in flight on a 10 deg transition cone tested previously in 23 wind tunnels. The cone was mounted on the nose of an F-15 aircraft and flown at Mach numbers room 0.5 to 2.0 and altitudes from 1500 meters (5000 feet) to 15,000 meters (50,000 feet), overlapping the Mach number/Reynolds number envelope of the wind tunnel tests. Transition was detected using a traversing pitot probe in contact with the surface. Data were obtained near zero cone incidence and adiabatic wall temperature. Transition Reynolds number was found to be a function of Mach number and of the ratio of wall temperature to adiabatic all temperature. Microphones mounted flush with the cone surface measured free-stream disturbances imposed on the laminar boundary layer and identified Tollmien-Schlichting waves as the probable cause of transition. Transition Reynolds number also correlated with the disturbance levels as measured by the cone surface microphones under a laminar boundary layer as well as the free-stream impact

Density Matrix Renormalization Group Method for the Random Quantum One-Dimensional Systems - Application to the Random Spin-1/2 Antiferromagnetic Heisenberg Chain -

The density matrix renormalization group method is generalized to one dimensional random systems. Using this method, the energy gap distribution of the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The results are consistent with the predictions of the renormalization group theory demonstrating the effectiveness of the present method in random systems. The possible application of the present method to other random systems is discussed.Comment: 13 pages, 3 figures upon reques

Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. II. Quasi-Equilibrium Regime of Spin Auto-Correlation Function

Using Monte Carlo simulations, we have studied isothermal aging of three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation function. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of {\it effective stiffness} for droplet excitations in the presence of domain walls. Within the range of computational time window, we have confirmed that the effective stiffness follows the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls, whose growth law has been extracted from our simulated data. Implication of the results are discussed in relation to experimental works on ac susceptibilities.Comment: 18 pages, 6 figure

Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains

The low-energy properties of a system at a critical point may have additional symmetries not present in the microscopic Hamiltonian. This letter presents the theory of a class of multicritical points that provide an interesting example of this in the phase diagrams of random antiferromagnetic spin chains. One case provides an analytic theory of the quantum critical point in the random spin-3/2 chain, studied in recent work by Refael, Kehrein and Fisher (cond-mat/0111295).Comment: Revtex, 4 pages (2 column format), 2 eps figure

Numerical Results for the Ground-State Interface in a Random Medium

The problem of determining the ground state of a $d$-dimensional interface embedded in a $(d+1)$-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energy exponent being $\theta = 0.84 \pm 0.03, 1.45 \pm 0.04$, in $d = 2, 3$, respectively. These results are compared with previous analytical and numerical estimates.Comment: 10 pages, REVTEX3.0; 3 ps files (separate:tar/gzip/uuencoded) for figure

Fluctuating loops and glassy dynamics of a pinned line in two dimensions

We represent the slow, glassy equilibrium dynamics of a line in a two-dimensional random potential landscape as driven by an array of asymptotically independent two-state systems, or loops, fluctuating on all length scales. The assumption of independence enables a fairly complete analytic description. We obtain good agreement with Monte Carlo simulations when the free energy barriers separating the two sides of a loop of size L are drawn from a distribution whose width and mean scale as L^(1/3), in agreement with recent results for scaling of such barriers.Comment: 11 pages, 4 Postscript figure

Can crack front waves explain the roughness of cracks ?

We review recent theoretical progress on the dynamics of brittle crack fronts and its relationship to the roughness of fracture surfaces. We discuss the possibility that the intermediate scale roughness of cracks, which is characterized by a roughness exponent approximately equal to 0.5, could be caused by the generation, during local instabilities by depinning, of diffusively broadened corrugation waves, which have recently been observed to propagate elastically along moving crack fronts. We find that the theory agrees plausibly with the orders of magnitude observed. Various consequences and limitations, as well as alternative explanations, are discussed. We argue that another mechanism, possibly related to damage cavity coalescence, is needed to account for the observed large scale roughness of cracks that is characterized by a roughness exponent approximately equal to 0.8Comment: 26 pages, 3 .eps figure. Submitted to J. Mech. Phys. Solid