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

On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses

We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system, we analyze the average link overlap, the probability distribution of window overlaps (among ground states computed with different boundary conditions) and the spatial overlap and link overlap correlation functions. We establish that the picture based on Replica Symmetry Breaking correctly describes the behavior of 3D Spin Glasses.Comment: 25 pages with 11 ps figures include

Inherent Structures in m-component Spin Glasses

We observe numerically the properties of the infinite-temperature inherent structures of m-component vector spin glasses in three dimensions. An increase of m implies a decrease of the amount of minima of the free energy, down to the trivial presence of a unique minimum. For little m correlations are small and the dynamics are quickly arrested, while for larger m low-temperature correlations crop up and the convergence is slower, to a limit that appears to be related with the system size.Comment: Version accepted in Phys. Rev. B, 10 pages, 11 figure

On the origin of ultrametricity

In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural assumptions: each replica is equivalent to the others (replica equivalence or stochastic stability) and all the mutual information about a pair of equilibrium configurations is encoded in their mutual distance or overlap (separability or overlap equivalence).Comment: 13 pages, 1 figur

A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model

In this paper we study the fluctuations of the probability distributions of the overlap in mean field spin glasses in the presence of a magnetic field on the De Almeida-Thouless line. We find that there is a large tail in the left part of the distribution that is dominated by the contributions of rare samples. Different techniques are used to examine the data and to stress on different aspects of the contribution of rare samples.Comment: 13 pages, 11 figure

Replica analysis of partition-function zeros in spin-glass models

We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distribution of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.Comment: 23 pages, 12 figures; minor change

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

Violation of the Fluctuation Dissipation Theorem in Finite Dimensional Spin Glasses

We study the violation of the fluctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry directly from equilibrium simulations. The two functions are numerically equal and in this way we have established that the conjectured connection between the violation of fluctuation dissipation theorem in the off-equilibrium dynamics and the replica symmetry breaking at equilibrium holds for finite dimensional spin glasses. These results point to a spin glass phase with spontaneously broken replica symmetry in finite dimensional spin glasses.Comment: 13 pages, 4 figures, also available at http://chimera.roma1.infn.it/index_papers_complex.htm

Fluctuations in the random-link matching problem

Using the replica approach and the cavity method, we study the fluctuations of the optimal cost in the random-link matching problem. By means of replica arguments, we derive the exact expression of its variance. Moreover, we study the large deviation function, deriving its expression in two different ways, namely using both the replica method and the cavity method.Comment: 9 pages, 3 figure