Off-Equilibrium Dynamics of a 4D Spin Glass with Asymmetric Couplings

We study the off-equilibrium dynamics of the Edwards-Anderson spin glass in four dimensions under the influence of a non-hamiltonian perturbation. We find that for small asymmetry the model behaves as the hamiltonian one, while for large asymmetry the behaviour of the model can be well described by an interrupted aging scenario. The autocorrelation function C(t_w+\tau,t_w) scales as \tau/t_w^\beta, with \beta a function of the asymmetry. For very long waiting times the previous regime crosses over to a time translational invariant regime (TTI) with stretched exponential relaxation. The model does not show signs of reaching a TTI regime for weak asymmetry, but in the aging regime the exponent \beta is always different from one, showing a non trivial aging scenario.Comment: Latex, 12 pages, 9 figure

Comment on "General Method to Determine Replica Symmetry Breaking Transitions"

In a recent letter Marinari et al [Phys. Rev. Lett. 81, 1698 (1998)] introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method unambiguously shows that replica symmetry breaking (RSB) occurs in short-range spin glasses. In this comment we show that while the new method is indeed useful for studying transitions in systems where TRS is absent (such as the p-spin model studied by them), the conclusion that it shows the existence of RSB in short-range spin glasses is wrong.Comment: 1 page, RevTe

Low T Dynamical Properties of Spin Glasses Smoothly Extrapolate to T=0

We compare ground state properties of 3D Ising Spin Glasses with Gaussian couplings with results from off-equilibrium numerical simulations at non zero (but low) temperatures. We find that the non-zero temperature properties of the system smoothly connect to the T=0 behavior, confirming the point of view that results established at T=0 typically also give relevant information about the $T\ne 0$ physics of the system.Comment: 14 pages and 4 ps figure

Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition

We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behaviour for strong values of the couplings. We also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For the spin glass in a field the maximum of non-self-averaging follows for given system size a line that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte-Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica-symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the one-step replica symmetry approach breaking predicts two transitions, the first transition being dynamical and the second thermodynamical. Our results suggest that in real finite dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.Comment: 11 pages, 11 figure

Numerical simulations on the 4d Heisenberg spin glass

We study the 4d Heisenberg spin glass model with Gaussian nearest-neighbor interactions. We use finite size scaling to analyze the data. We find a behavior consistent with a finite temperature spin glass transition. Our estimates for the critical exponents agree with the results from epsilon-expansion.Comment: 11 pages, LaTeX, preprint ROMA1 n. 105

Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses

We compute numerically small window overlaps in the three dimensional Edwards Anderson spin glass. We show that they behave in the way implied by the Replica Symmetry Breaking Ansatz, that they do not qualitatively differ from the full volume overlap and do not tend to a trivial function when increasing the lattice volume. On the contrary we show they are affected by small finite volume effects, and are interesting tools for the study of the features of the spin glass phase.Comment: 9 pages plus 5 figure

The Fully Frustrated Hypercubic Model is Glassy and Aging at Large DD

We discuss the behavior of the fully frustrated hypercubic cell in the infinite dimensional mean-field limit. In the Ising case the system undergoes a glass transition, well described by the random orthogonal model. Under the glass temperature aging effects show clearly. In the $XY$ case there is no sign of a phase transition, and the system is always a paramagnet.Comment: Figures added in uufiles format, and epsf include

The mean field infinite range p=3 spin glass: equilibrium landscape and correlation time scales

We investigate numerically the dynamical behavior of the mean field 3-spin spin glass model: we study equilibrium dynamics, and compute equilibrium time scales as a function of the system size V. We find that for increasing volumes the time scales $\tau$ increase like $\ln \tau \propto V$. We also present an accurate study of the equilibrium static properties of the system.Comment: 6 pages, 9 figure

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

On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses

We compute and analyze couples of ground states of 3D spin glasses before and after applying a volume perturbation which adds to the Hamiltonian a repulsion from the true ground state. The physical picture based on Replica Symmetry Breaking is in excellent agreement with the observed behavior.Comment: 4 pages including 5 .ps figure