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

Distributions of gaps and end-to-end correlations in random transverse-field Ising spin chains

A previously introduced real space renormalization-group treatment of the random transverse-field Ising spin chain is extended to provide detailed information on the distribution of the energy gap and the end-to-end correlation function for long chains with free boundary conditions. Numerical data, using the mapping of the problem to free fermions, are found to be in good agreement with the analytic finite size scaling predictions.Comment: 12 pages revtex, 10 figures, submitted to Phys. Rev.

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

Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic changes which arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptation, v, in several models of such sexual populations and show that v is linear in NU_b only in sufficiently small populations. In large populations, v increases much more slowly as log NU_b. The prefactor of this logarithm, however, increases as the square of the recombination rate. This acceleration of adaptation by recombination implies a strong evolutionary advantage of sex

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

Stability of Elastic Glass Phases in Random Field XY Magnets and Vortex Lattices in Type II Superconductors

A description of a dislocation-free elastic glass phase in terms of domain walls is developed and used as the basis of a renormalization group analysis of the energetics of dislocation loops added to the system. It is found that even after optimizing over possible paths of large dislocation loops, their energy is still very likely to be positive when the dislocation core energy is large. This implies the existence of an equilibrium elastic glass phase in three dimensional random field X-Y magnets, and a dislocation free, bond-orientationally ordered ``Bragg glass'' phase of vortices in dirty Type II superconductors.Comment: 12 pages, Revtex, no figures, submitted to Phys Rev Letter

Quantum Collective Creep: a Quasiclassical Langevin Equation Approach

The dynamics of an elastic medium driven through a random medium by a small applied force is investigated in the low-temperature limit where quantum fluctuations dominate. The motion proceeds via tunneling of segments of the manifold through barriers whose size grows with decreasing driving force $f$. In the limit of small drive, at zero-temperature the average velocity has the form $v\propto\exp[-{\rm const.}/\hbar^{\alpha} f^{\mu}]$. For strongly dissipative dynamics, there is a wide range of forces where the dissipation dominates and the velocity--force characteristics takes the form $v\propto\exp[-S(f)/\hbar]$, with $S(f)\propto 1/ f^{(d+2\zeta)/(2-\zeta)}$ the action for a typical tunneling event, the force dependence being determined by the roughness exponent $\zeta$ of the $d$-dimensional manifold. This result agrees with the one obtained via simple scaling considerations. Surprisingly, for asymptotically low forces or for the case when the massive dynamics is dominant, the resulting quantum creep law is {\it not} of the usual form with a rate proportional to $\exp[-S(f)/\hbar]$; rather we find $v\propto \exp\{-[S(f)/\hbar]^2\}$ corresponding to $\alpha=2$ and $\mu= 2(d+2\zeta-1)/(2-\zeta)$, with $\mu/2$ the naive scaling exponent for massive dynamics. Our analysis is based on the quasi-classical Langevin approximation with a noise obeying the quantum fluctuation--dissipation theorem. The many space and time scales involved in the dynamics are treated via a functional renormalization group analysis related to that used previously to treat the classical dynamics of such systems. Various potential difficulties with these approaches to the multi-scale dynamics -- both classical and quantum -- are raised and questions about the validity of the results are discussed.Comment: RevTeX, 30 pages, 8 figures inserte

An Inversion Method for Measuring Beta in Large Redshift Surveys

A precision method for determining the value of Beta= Omega_m^{0.6}/b, where b is the galaxy bias parameter, is presented. In contrast to other existing techniques that focus on estimating this quantity by measuring distortions in the redshift space galaxy-galaxy correlation function or power spectrum, this method removes the distortions by reconstructing the real space density field and determining the value of Beta that results in a symmetric signal. To remove the distortions, the method modifies the amplitudes of a Fourier plane-wave expansion of the survey data parameterized by Beta. This technique is not dependent on the small-angle/plane-parallel approximation and can make full use of large redshift survey data. It has been tested using simulations with four different cosmologies and returns the value of Beta to +/- 0.031, over a factor of two improvement over existing techniques.Comment: 16 pages including 6 figures Submitted to The Astrophysical Journa