arXiv subjects
Publications and source records attributed to E. Marinari.
We discuss temperature chaos in mean field and realistic 3D spin glasses. Our numerical simulations show no trace of a temperature chaotic behavior for the system sizes considered. We discuss the experimental and theoretical implications of these findings.
In a comment cond-mat/9811080 to our paper (PRL, vol 81, 1698 (1998)) H. Bokil, A. Bray, B. Drossel and M. Moore claimed that we have reached wrong conclusions. We show here why their claims are not correct, especially when compared to the analysis of reference cond-mat/9808140.
In ref. cond-mat/9811419 Houdayer and Martin analyze the T=0 3d EA spin glass with a magnetic field $B$. By using a new, powerful method, they determine an effective critical field $B_c$ as a function of the lattice size $L$. They use their results to deduce that the model is behaving like in the droplet approach and not like the mean-field theory. We show here, by using some unpublished data, that this very interesting method and numerical results are completely compatible with the behavior implied by the Replica Symmetry Breaking theory.
In a recent letter Moore et al. claim to exhibit evidence for a non-mean-field behavior of the $3d$ Ising spin glass. We show that their claim is insubstantial, and by analyzing in detail the behavior of the Migdal-Kadanoff approximation (MKA) as compared to the behavior of the Edwards-Anderson (EA) spin glass we find further evidence of a mean-field like behavior of the $3d$ spin glass.
We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three dimensional spin glasses.
We study numerically a disordered model that interpolates among the Sherrington-Kirkpatrick mean field model and the three dimensional Edwards-Anderson spin glass. We find that averages over the disorder of powers of the overlap and of the full $P(q)$ are smooth, and do not show any discontinuity. Different lattice sizes are used to provide evidence for a smooth behavior of disorder averages in the thermodynamic limit. Quantities defined on a given realization of the disorder show a chaotic behavior. Our results support the validity of a Replica Symmetry Breaking description of finite dimensional models.
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.
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.
We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest concerns models where this symmetry is absent. We apply the method to long-range and short-range Ising spin glasses with and without magnetic field as well as short-range multispin interaction spin glasses.
I discuss results from numerical simulations of finite dimensional spin glass models, and show that they show all signatures of a mean field like behavior, basically coinciding with the one of the Parisi solution. I discuss the Binder cumulant, the probability distribution of the order parameter, the non self-averaging behavior. The determination of correlation function and of spatially blocked observables quantities helps in qualifying the behavior of the system.
By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out the behavior of the system in limit where both $t$ and $V$ go to infinity, but where the limit $V \to \infty$ is taken first. By showing that the dynamic overlap $q$ converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with the ones obtained by mean field computations.
We study the dynamics of the SK model modified by a small non-hamiltonian perturbation. We study aging, and we find that on the time scales investigated by our numerical simulations it survives a small perturbation (and is destroyed by a large one). If we assume we are observing a transient behavior the scaling of correlation times versus the asymmetry strength is not compatible with the one expected for the spherical model. We discuss the slow power law decay of observable quantities to equilibrium, and we show that for small perturbations power like decay is preserved. We also discuss the asymptotically large time region on small lattices.
We study the dynamical out-of-equilibrium behavior of a $J = \pm 1$ Ising spin glass on quenched $ϕ^{3}$ graphs. We show that magnetization and energy decay with a power law behavior, with exponents that are linear in $\frac{T}{T_{c}}$. Quenched $ϕ^{3}$ graphs turn out to be a very effective way to study numerically mean field spin glasses.
We introduce a new numerical technique to compute mass spectra, based on difference method and on a new gauge fixing procedure. We show that the method is very effective by test runs on a $SU(2)$ lattice gauge theory.
By numerical simulations of the $3d$ Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.
We show that computing the coefficients of the Taylor expansion of the solution of the off-equilibrium dynamical equations characterizing models with quenched disorder is a very effective way to understand the long time asymptotic behavior. We study the $p=3$ spherical spin glass model, and we compute the asymptotic energy (in the critical region and down to $T=0$) and the coefficients of the time decay of the energy.
We examine the geometrical and topological properties of surfaces surrounding clusters in the 3--$d$ Ising model. For geometrical clusters at the percolation temperature and Fortuin--Kasteleyn clusters at $T_c$, the number of surfaces of genus $g$ and area $A$ behaves as $A^{x(g)}e^{-μ(g)A}$, with $x$ approximately linear in $g$ and $μ$ constant. These scaling laws are the same as those we obtain for simulations of 3--$d$ bond percolation. We observe that cross--sections of spin domain boundaries at $T_c$ decompose into a distribution $N(l)$ of loops of length $l$ that scales as $l^{-τ}$ with $τ\sim 2.2$. We also present some new numerical results for 2--$d$ self-avoiding loops that we compare with analytic predictions. We address the prospects for a string--theoretic description of cluster boundaries.
Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues. One is that contrary to recent claims there is strong analytical and numerical evidence for the existence of an exponential bound that makes the partition function well-defined. The other is that there may be an ambiguity in the choice of the measure of the discrete model which could even lead to the existence of different universality classes.