Related papers: Random Overlap Structures: Properties and Applicat…
We consider short-range classical spin glasses, or other disordered systems, consisting of Ising spins. For a low-temperature Gibbs state in infinite size in such a system, for given random bonds, it is controversial whether its…
In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can…
We present results of recent high-statistics Monte Carlo simulations of the Edwards-Anderson Ising spin-glass model in three and four dimensions. The study is based on a non-Boltzmann sampling technique, the multi-overlap algorithm which is…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
We study invariant measures for random countable (finite or infinite) conformal iterated function systems (IFS) with arbitrary overlaps. We do not assume any type of separation condition. We prove, under a mild assumption of finite entropy,…
We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spin-glass quenched state. We show that stochastic stability holds in beta-average for…
The main result in this paper is motivated by the M\'ezard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random K-sat model. Using the fact that one…
In order to study certain questions concerning the distribution of the overlap in Sherrington--Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with…
We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic…
In this paper I introduce the probability distribution of the local overlap in spin glasses. The properties of the local overlaps are studied in details. These quantities are related to the recently proposed local version of the fluctuation…
We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations we explicitly construct a constrained replica free energy functional that maps directly…
The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by…
The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…
The statistical properties of the local optima (metastable states) of the infinite range Ising spin glass with p-spin interactions in the presence of an external magnetic field h are investigated analytically. The average number of optima…
The Potts spin glass is a generalization of the Sherrington--Kirkpatrick (SK) model that allows for spins to take more than two values. Based on a novel synchronization mechanism, Panchenko (2018) showed that the limiting free energy is…
We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
We study a class of Gibbs measures of classical particle spin systems with spin space $S=\mathbb{R}^{m}$ and unbounded pair interaction, living on a metric graph given by a typical realization $\gamma $ of a random point process in…