Low Energy Excitations in Spin Glasses from Exact Ground States

We investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a coupling-dependent perturbation introduced previously. The ground states are determined exactly for system sizes up to 12^3 spins using a branch and cut algorithm. The data are consistent with a picture where the surface of the excitations is not space-filling, such as the droplet or the ``TNT'' picture, with only minimal corrections to scaling. When allowing for very large corrections to scaling, the data are also consistent with a picture with space-filling surfaces, such as replica symmetry breaking. The energy of the excitations scales with their size with a small exponent \theta', which is compatible with zero if we allow moderate corrections to scaling. We compare the results with data for periodic boundary conditions obtained with a genetic algorithm, and discuss the effects of different boundary conditions on corrections to scaling. Finally, we analyze the performance of our branch and cut algorithm, finding that it is correlated with the existence of large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with more discussion of the numerical data. Fig.11 adde

Randomly dilute Ising model: A nonperturbative approach

The N-vector cubic model relevant, among others, to the physics of the randomly dilute Ising model is analyzed in arbitrary dimension by means of an exact renormalization-group equation. This study provides a unified picture of its critical physics between two and four dimensions. We give the critical exponents for the three-dimensional randomly dilute Ising model which are in good agreement with experimental and numerical data. The relevance of the cubic anisotropy in the O(N) model is also treated.Comment: 4 pages, published versio

Equilibrium valleys in spin glasses at low temperature

We investigate the 3-dimensional Edwards-Anderson spin glass model at low temperature on simple cubic lattices of sizes up to L=12. Our findings show a strong continuity among T>0 physical features and those found previously at T=0, leading to a scenario with emerging mean field like characteristics that are enhanced in the large volume limit. For instance, the picture of space filling sponges seems to survive in the large volume limit at T>0, while entropic effects play a crucial role in determining the free-energy degeneracy of our finite volume states. All of our analysis is applied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First, we consider the spatial properties of the sites where pairs of independent spin configurations differ and we introduce a modified spin overlap distribution which exhibits a non-trivial limit for large L. Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations into valleys. On average these valleys have free-energy differences of O(1), but a difference in the (extensive) internal energy that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by sponge-like space filling clusters, just as found previously for low-energy system-size excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional reference

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

The three-dimensional randomly dilute Ising model: Monte Carlo results

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining $\nu = 0.683(3)$, $\eta = 0.035(2)$, $\beta = 0.3535(17)$, and $\alpha = -0.049(9)$, in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio $R^+_\xi$ that expresses the universality of the free-energy density per correlation volume. We find $R^+_\xi = 0.2885(15)$.Comment: 34 pages, 7 figs, few correction

Ultrametricity in 3D Edwards-Anderson spin glasses

We perform an accurate test of Ultrametricity in the aging dynamics of the three dimensional Edwards-Anderson spin glass. Our method consists in considering the evolution in parallel of two identical systems constrained to have fixed overlap. This turns out to be a particularly efficient way to study the geometrical relations between configurations at distant large times. Our findings strongly hint towards dynamical ultrametricity in spin glasses, while this is absent in simpler aging systems with domain growth dynamics. A recently developed theory of linear response in glassy systems allows to infer that dynamical ultrametricity implies the same property at the level of equilibrium states.Comment: 4 pages, 5 figure

Domain growth and aging scaling in coarsening disordered systems

Using extensive Monte Carlo simulations we study aging properties of two disordered systems quenched below their critical point, namely the two-dimensional random-bond Ising model and the three-dimensional Edwards-Anderson Ising spin glass with a bimodal distribution of the coupling constants. We study the two-times autocorrelation and space-time correlation functions and show that in both systems a simple aging scenario prevails in terms of the scaling variable $L(t)/L(s)$, where $L$ is the time-dependent correlation length, whereas $s$ is the waiting time and $t$ is the observation time. The investigation of the space-time correlation function for the random-bond Ising model allows us to address some issues related to superuniversality.Comment: 8 pages, 9 figures, to appear in European Physical Journal

Off-equilibrium fluctuation-dissipation relations in the 3d Ising Spin Glass in a magnetic field

We study the fluctuation-dissipation relations for a three dimensional Ising spin glass in a magnetic field both in the high temperature phase as well as in the low temperature one. In the region of times simulated we have found that our results support a picture of the low temperature phase with broken replica symmetry, but a droplet behavior can not be completely excluded.Comment: 9 pages, 11 ps figures, revtex. Final version to be published in Phys. Rev.

Extended droplet theory for aging in short-ranged spin glasses and a numerical examination

We analyze isothermal aging of a four dimensional Edwards-Anderson model in detail by Monte Carlo simulations. We analyze the data in the view of an extended version of the droplet theory proposed recently (cond-mat/0202110) which is based on the original droplet theory plus conjectures on the anomalously soft droplets in the presence of domain walls. We found that the scaling laws including some fundamental predictions of the original droplet theory explain well our results. The results of our simulation strongly suggest the separation of the breaking of the time translational invariance and the fluctuation dissipation theorem in agreement with our scenario.Comment: 27 pages, 39 epsfiles, revised versio

Chaotic, memory and cooling rate effects in spin glasses: Is the Edwards-Anderson model a good spin glass?

We investigate chaotic, memory and cooling rate effects in the three dimensional Edwards-Anderson model by doing thermoremanent (TRM) and AC susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of re-initialization processes in temperature change experiments (TRM or AC). A detailed comparison with AC relaxation experiments in the presence of DC magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.Comment: 17 pages, 10 figures. The original version of the paper has been split in two parts. The second part is now available as cond-mat/010224