Related papers: Spin glasses and the Parisi formula
Considering the unphysical result obtained in the calculation of the free-energy cost for twisting the boundary conditions in a spin glass, we trace it to the negative multiplicities associated with the Parisi replica-symmetry breaking…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
An introduction and overview is given of the theory of spin glasses and its application.
We provide rigorous proofs which show that the main features of the Parisi solution of the Sherrington-Kirkpatrick spin glass are not valid for more realistic spin glass models in any dimension and at any temperature.
The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation,…
Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the…
In these two lectures I review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two…
The East model is a particular one dimensional interacting particle system in which certain transitions are forbidden according to some constraints depending on the configuration of the system. As such it has received particular attention…
We review the most striking experimental results on aging in a variety of disordered systems, which reveal similar features but also important differences. We argue that a generic model that reproduce many of these features is that of {\it…
A brief personal perspective is given of issues, questions, formulations, methods, some answers and selected extensions posed by the spin glass problem, showing how considerations of an apparently insignificant and practically unimportant…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
We study numerically the three-dimensional $\phi^{4}$ spin glass, a prototypical disordered and discretized Euclidean field theory that manifests inhomogeneities in space and time but considers a homogeneous squared mass and lambda terms.…
The behavior of a newly introduced overlap parameter is analyzed, measuring the correlation between intensity fluctuations of waves in random media in different physical regimes, with varying amount of disorder and non-linearity. Its…
We propose an indirect way of studying the fluctuation-dissipation relation in spin-glasses that only uses available susceptibility data. It is based on a dynamic extension of the Parisi-Toulouse approximation and a Curie-Weiss treatment of…
Spin glasses are systems whose magnetic moments freeze at low temperature into random orientations without long-range order. It is generally accepted that both frustration and disorder are essential ingredients in all spin glasses, so it…
In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of…
This paper aims to establish a connection between Pisarski's fixed point and a (2+3)-spin-glass model with sextic confinement potential. This is made possible by the unconventional power-counting induced by the effective kinetics provided…
We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly…