8,251 research outputs found

    On the origin of ultrametricity

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    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

    DD-dimensional Arrays of Josephson Junctions, Spin Glasses and qq-deformed Harmonic Oscillators

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    We study the statistical mechanics of a DD-dimensional array of Josephson junctions in presence of a magnetic field. In the high temperature region the thermodynamical properties can be computed in the limit D→∞D \to \infty, where the problem is simplified; this limit is taken in the framework of the mean field approximation. Close to the transition point the system behaves very similar to a particular form of spin glasses, i.e. to gauge glasses. We have noticed that in this limit the evaluation of the coefficients of the high temperature expansion may be mapped onto the computation of some matrix elements for the qq-deformed harmonic oscillator

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

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    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 Glassy Potts Model

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    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 TcT_c down to T=0. We study numerical the 4 dimensional model with q=4q=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

    Liquid-glass transition in equilibrium

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    We show in numerical simulations that a system of two coupled replicas of a binary mixture of hard spheres undergoes a phase transition in equilibrium at a density slightly smaller than the glass transition density for an unreplicated system. This result is in agreement with the theories that predict that such a transition is a precursor of the standard ideal glass transition. The critical properties are compatible with those of an Ising system. The relations of this approach to the conventional approach based on configurational entropy are briefly discussed.Comment: 5 pages, 3 figures, version accepted for publication in the Physical Review

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

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    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

    The K-sat problem in a simple limit

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    We compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computations can be strongly simplified and the thermodynamical properties can be obtained with an high accuracy. We find evidence for a continuous replica symmetry breaking in the region of high number of clauses, α>αc\alpha > \alpha_c.Comment: 9 pages, 6 figures. To appear in J. Stat. Phys. Minor change
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