General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity

For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas, let us say a, and the added s+1 is either independent of the former ones, or it is identical to one of the overlaps q(a,b), with b running among the first s replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical and General. Also available at http://rerumnatura.zool.su.se/stefano/ms/ghigu.p

Comparison of the Spherical Averaged Pseudopotential Model with the Stabilized Jellium Model

We compare Kohn-Sham results (density, cohesive energy, size and effect of charging) of the Spherical Averaged Pseudopotential Model with the Stabilized Jellium Model for clusters of sodium and aluminum with less than 20 atoms. We find that the Stabilized Jellium Model, although conceptually and practically more simple, gives better results for the cohesive energy and the elastic stiffness. We use the Local Density Approximation as well as the Generalized Gradient Approximation to the exchange and correlation energies.Comment: 13 pages, latex, 8 figures, compressed postscript version available at http://www.fis.uc.pt/~vieir

Opinion and community formation in coevolving networks

In human societies opinion formation is mediated by social interactions, consequently taking place on a network of relationships and at the same time influencing the structure of the network and its evolution. To investigate this coevolution of opinions and social interaction structure we develop a dynamic agent-based network model, by taking into account short range interactions like discussions between individuals, long range interactions like a sense for overall mood modulated by the attitudes of individuals, and external field corresponding to outside influence. Moreover, individual biases can be naturally taken into account. In addition the model includes the opinion dependent link-rewiring scheme to describe network topology coevolution with a slower time scale than that of the opinion formation. With this model comprehensive numerical simulations and mean field calculations have been carried out and they show the importance of the separation between fast and slow time scales resulting in the network to organize as well-connected small communities of agents with the same opinion.Comment: 10 pages, 5 figures. New inset for Fig. 1 and references added. Submitted to Physical Review

A Monte Carlo study of Inverse Symmetry Breaking

We make a Monte Carlo study of the coupled two-scalar $\lambda\phi^2_1\phi^2_2$ model in four dimensions at finite temperature. We find no trace of Inverse Symmetry Breaking for values of the renormalized parameters for which perturbation theory predicts this phenomenon.Comment: 4 pages, revtex, 3 figures include

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

On the Phase Structure of the 3D Edwards Anderson 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.Comment: 30 pages and 17 figures. Final version to be published in PR

Study of the phase transition in the 3d Ising spin glass from out of equilibrium numerical simulations

Using the decay of the out equilibrium spin-spin correlation function we compute the equilibrium Edward-Anderson order parameter in the three dimensional binary Ising spin glass in the spin glass phase. We have checked that the Edward-Anderson order parameter computed from out of equilibrium numerical simulations follows with good precision the critical law as determined in experiments and in numerical studies at equilibrium. We have also studied the dependence of the order parameter with the lattice size. Finally we present a large time study of the scaling of the off-equilibrium fluctuation-dissipation relations.Comment: 14 pages, 7 Postscript figure

Phase Transition of XY Model in Heptagonal Lattice

We numerically investigate the nature of the phase transition of the XY model in the heptagonal lattice with the negative curvature, in comparison to other interaction structures such as a flat two-dimensional (2D) square lattice and a small-world network. Although the heptagonal lattice has a very short characteristic path length like the small-world network structure, it is revealed via calculation of the Binder's cumulant that the former exhibits a zero-temperature phase transition while the latter has the finite-temperature transition of the mean-field nature. Through the computation of the vortex density as well as the correlation function in the low-temperature approximation, we show that the absence of the phase transition originates from the strong spinwave-type fluctuation, which is discussed in relation to the usual 2D XY model.Comment: 5 pages, 6 figures, to be published in Europhys. Let

Matching microscopic and macroscopic responses in glasses

We first reproduce on the Janus and Janus II computers a milestone experiment that measures the spin-glass coherence length through the lowering of free-energy barriers induced by the Zeeman effect. Secondly we determine the scaling behavior that allows a quantitative analysis of a new experiment reported in the companion Letter [S. Guchhait and R. Orbach, Phys. Rev. Lett. 118, 157203 (2017)]. The value of the coherence length estimated through the analysis of microscopic correlation functions turns out to be quantitatively consistent with its measurement through macroscopic response functions. Further, non-linear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length.Comment: 6 pages, 4 figure

The Mpemba effect in spin glasses is a persistent memory effect

The Mpemba effect occurs when a hot system cools faster than an initially colder one, when both are refrigerated in the same thermal reservoir. Using the custom built supercomputer Janus II, we study the Mpemba effect in spin glasses and show that it is a non-equilibrium process, governed by the coherence length \xi of the system. The effect occurs when the bath temperature lies in the glassy phase, but it is not necessary for the thermal protocol to cross the critical temperature. In fact, the Mpemba effect follows from a strong relationship between the internal energy and \xi that turns out to be a sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents itself as an intriguing new avenue for the experimental study of the coherence length in supercooled liquids and other glass formers.Comment: Version accepted for publication in PNAS. 6 pages, 7 figure