Related papers: Random Matrices and complexity of Spin Glasses
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…
In a companion paper we developed the generalized TAP approach for general multi-species spherical mixed $p$-spin models. In this paper, we use it to compute the limit of the free energy at any temperature for all pure multi-species…
We study the Langevin dynamics for spherical $p$-spin models, focusing on the short time regime described by the Cugliandolo-Kurchan equations. Confirming a prediction of [Cugliandolo-Kurchan, Phys. Rev. Lett. 1993], we show the asymptotic…
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…
A random matrix approach to glassy physics is introduced. It leads to a class of models which exhibit both, glassy low-temperature phases, and double-- and single-well configurations in their potential energy. The distribution of parameters…
The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory I discuss how to…
The `lid' algorithm performs an exhaustive exploration of neighborhoods of local energy minima of energy landscapes. This paper describes an implementation of the algorithm, including issues of parallel performance and scalability. To…
Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,... All these topics share certain relations, called "loop equations" or…
We numerically address the issue of how the ground state topology is reflected in the finite temperature dynamics of the $\pm J$ Edwards-Anderson spin glass model. In this system a careful study of the ground state configurations allows to…
Across many scientific and engineering disciplines, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of $\pm J$ spin glasses at zero…
We study the classical 1D Heisenberg spin glasses. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from first…
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…
The large N infinite range spin glass is considered, in particular the number of spin components k needed to form the ground state and the sample-to-sample fluctuations in the Lagrange multiplier field on each site. The physical…
Let ${\boldsymbol A}\in{\mathbb R}^{n\times n}$ be a symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing $\langle{\boldsymbol \sigma},{\boldsymbol…
We study the random energy model with a hierarchical structure known as the generalized random energy model (GREM). In contrast to the original analysis by the microcanonical ensemble formalism, we investigate the GREM by the canonical…
We study the dynamics of a quantum $p$-spin glass model starting from initial states defined in microcanonical shells, in a classical regime. We compute different chaos estimators, such as the Lyapunov exponent and the Kolmogorov-Sinai…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A…
We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…