Real space application of the mean-field description of spin glass dynamics

The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard `mean-field theory' versus `droplet picture' debate of the last decades. The main predictions of both theories concerning the spin glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of the spin glass coherence length which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed.Comment: 4 pages, 4 eps figures. v2: published versio

Critical phenomena in a highly constrained classical spin system: Neel ordering from the Coulomb phase

Many classical, geometrically frustrated antiferromagnets have macroscopically degenerate ground states. In a class of three-dimensional systems, the set of degenerate ground states has power-law correlations and is an example of a Coulomb phase. We investigate Neel ordering from such a Coulomb phase, induced by weak additional interactions that lift the degeneracy. We show that the critical point belongs to a universality class that is different from the one for the equivalent transition out of the paramagnetic phase, and that it is characterised by effective long-range interactions; alternatively, ordering may be discontinuous. We suggest that a transition of this type may be realised by applying uniaxial stress to a pyrochlore antiferromagnet.Comment: 4 pages, 3 figure

Universal Finite Size Scaling Functions in the 3D Ising Spin Glass

We study the three-dimensional Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Monte Carlo data are extrapolated to infinite volume with an iterative procedure up to correlation lengths xi \approx 140. The infinite volume data are consistent with a conventional power law singularity at finite temperature Tc. Taking into account corrections to scaling, we find Tc = 1.156 +/- 0.015, nu = 1.8 +/- 0.2 and eta = -0.26 +/- 0.04. The data are also consistent with an exponential singularity at finite Tc, but not with an exponential singularity at zero temperature.Comment: 4 pages, Revtex, 4 postscript figures include

The Glassy Potts Model

We introduce a Potts model with quenched, frustrated disorder, that enjoys of a gauge symmetry that forbids spontaneous magnetization, and allows the glassy phase to extend from $T_c$ down to T=0. We study numerical the 4 dimensional model with $q=4$ states. We show the existence of a glassy phase, and we characterize it by studying the probability distributions of an order parameter, the binder cumulant and the divergence of the overlap susceptibility. We show that the dynamical behavior of the system is characterized by aging.Comment: 4 pages including 4 (color) ps figures (all on page 4

Nature of the Spin-glass State in the Three-dimensional Gauge Glass

We present results from simulations of the gauge glass model in three dimensions using the parallel tempering Monte Carlo technique. Critical fluctuations should not affect the data since we equilibrate down to low temperatures, for moderate sizes. Our results are qualitatively consistent with earlier work on the three and four dimensional Edwards-Anderson Ising spin glass. We find that large scale excitations cost only a finite amount of energy in the thermodynamic limit, and that those excitations have a surface whose fractal dimension is less than the space dimension, consistent with a scenario proposed by Krzakala and Martin, and Palassini and Young.Comment: 5 pages, 7 figure

How the Replica-Symmetry-Breaking Transition Looks Like in Finite-Size Simulations

Finite-size effects in the mean-field Ising spin glass and the mean-field three-state Potts glass are investigated by Monte Carlo simulations. In the thermodynamic limit, each model is known to exhibit a continuous phase transition into the ordered state with a full and a one-step replica-symmetry breaking (RSB), respectively. In the Ising case, Binder parameter g calculated for various finite sizes remains positive at any temperature and crosses at the transition point, while in the Potts case g develops a negative dip without showing a crossing in the g>0 region. By contrast, non-self averaging parameters always remain positive and show a clear crossing at the transition temperature in both cases. Our finding suggests that care should be taken in interpreting the numerical data of the Binder parameter, particularly when the system exhibits a one-step-like RSB.Comment: 7 pages, 8 figure

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific heat exponent. We expect the nature of the transition in this 3-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.Comment: 19 pages, Latex, 16 ps figure

Localization of Denaturation Bubbles in Random DNA Sequences

We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to \AT-rich segments. In the localized regime, the bubbles exhibit ``aging'' and move around sub-diffusively with continuously varying dynamic exponents. These properties are derived using results of large-deviation theory together with scaling arguments, and are verified by Monte-Carlo simulations.Comment: TeX file with postscript figure

Classical and Quantum Behavior in Mean-Field Glassy Systems

In this talk I review some recent developments which shed light on the main connections between structural glasses and mean-field spin glass models with a discontinuous transition. I also discuss the role of quantum fluctuations on the dynamical instability found in mean-field spin glasses with a discontinuous transition. In mean-field models with pairwise interactions in a transverse field it is shown, in the framework of the static approximation, that such instability is suppressed at zero temperature.Comment: 9 Pages (including 5 Figures), Revtex, Proceedings of the XIV Sitges Conference, June 1996 (Barcelona) Spai

Evidence for the double degeneracy of the ground-state in the 3D ±J\pm J spin glass

A bivariate version of the multicanonical Monte Carlo method and its application to the simulation of the three-dimensional $\pm J$ Ising spin glass are described. We found the autocorrelation time associated with this particular multicanonical method was approximately proportional to the system volume, which is a great improvement over previous methods applied to spin-glass simulations. The principal advantage of this version of the multicanonical method, however, was its ability to access information predictive of low-temperature behavior. At low temperatures we found results on the three-dimensional $\pm J$ Ising spin glass consistent with a double degeneracy of the ground-state: the order-parameter distribution function $P(q)$ converged to two delta-function peaks and the Binder parameter approached unity as the system size was increased. With the same density of states used to compute these properties at low temperature, we found their behavior changing as the temperature is increased towards the spin glass transition temperature. Just below this temperature, the behavior is consistent with the standard mean-field picture that has an infinitely degenerate ground state. Using the concept of zero-energy droplets, we also discuss the structure of the ground-state degeneracy. The size distribution of the zero-energy droplets was found to produce the two delta-function peaks of $P(q)$.Comment: 33 pages with 31 eps figures include