Related papers: Spin glasses and the Parisi formula
We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They…
The nature of equilibrium states in disordered materials is often studied using an overlap function P(q), the probability of two configurations having similarity q. Exact sampling simulations of a two-dimensional proxy for three-dimensional…
Glass transition where viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics (Cavagna, 2009;…
Dilute magnetic nanoparticle systems exhibit slow dynamics [1] due to a broad distribution of relaxation times that can be traced to a correspondingly broad distribution of particle sizes [1]. However, at higher concentrations interparticle…
In these lectures I will review some theoretical results that have been obtained for spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will…
Ising spin glass models with bimodal, Gaussian, uniform and Laplacian interaction distributions in dimension five are studied through detailed numerical simulations. The data are analyzed in both the finite-size scaling regime and the…
In these notes, we continue our investigation of classical toy models of disordered statistical mechanics through various techniques recently developed and tested mainly on the paradigmatic SK spin glass. Here we consider the p-spin-glass…
Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits…
We prove a correlation type inequality for spin systems with quenched symmetric random interactions. This gives monotonicity of the pressure with respect to the strength of the interaction for a class of spin glass models. Consequences…
Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the characteristic large $x$ fall-off behavior $f(x)\sim\exp (-a…
We show that there is no need to modify the Parisi replica symmetry breaking ansatz, by working with $R$ steps of breaking and solving {\it exactly} the discrete stationarity equations generated by the standard ``truncated Hamiltonian" of…
Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g. in terms of pairwise dependences) - as in statistical learning - or because they capture the…
For the Edwards-Anderson Ising spin-glass model in three and four dimensions (3d and 4d) we have performed high statistics Monte Carlo calculations of those free-energy barriers $F^q_B$ which are visible in the probability density $P_J(q)$…
The one-dimensional long-range Ising spin glass provides useful insights into the properties of finite dimensional spin glasses with short-range interactions. The defect energy renormalization group equations derived for it by Kotliar,…
We introduce a mean field spin glass model with gaussian distribuited spins and pairwise interactions, whose couplings are drawn randomly from a normal gaussian distribution too. We completely control the main thermodynamical properties of…
This lecture deals with glassy dynamics and aging in disordered systems. Special emphasis is put on dynamic mean field theory. In the first part I present some of the systems of interest, in particular spin-glasses, supercooled liquids and…
In this work a short overview of the development of spin glass theories, mainly long and short range Ising models, are presented.
We give the explicit expression of the infinite volume limit for the random overlap structures appearing in the mean field spin glass model. These structures have the expected factorization property for the cavity fields, and enjoy…
We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion of a suitably perturbed average of the…
We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models.…