Related papers: Aspects of Statistical Physics in Computational Co…
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
Random constraint satisfaction problems are interesting model systems for spin-glasses and glassy dynamics studies. As the constraint density of such a system reaches certain threshold value, its solution space may split into extremely many…
We define a new family of random spin models with one-dimensional structure, finite-range multi-spin interactions, and bounded average degree (number of interactions in which each spin participates). Unfrustrated ground states can be…
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…
The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under…
This chapter introduces a variety of spin glass models, beyond the simple Sherrington-Kirkpatrick (SK) version, that have led to enriched understanding and application.
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…
Motivated by the recent development of quantum technology using quantum annealing technique and the recent works on the static properties of the Sherrington-Kirkpatrick (SK) spin glass model, we study quantum annealing of the spin glass…
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…
Spin glasses occupy a unique place in condensed matter: they freeze collectively while remaining struc-turally disordered, and they exhibit slow, history-dependent dynamics that reflect an exceptionally rug-ged free-energy landscape. This…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in…
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;…
This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the mean-field approximation, spin glasses and combinatorial…
We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…
The Ising $p$-spin glass and random $k$-SAT are two canonical examples of disordered systems that play a central role in understanding the link between geometric features of optimization landscapes and computational tractability. Both…
We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica…
We propose an expanded spin-glass model, called the quantum Ghatak-Sherrington model, which considers spin-1 quantum spin operators in a crystal field and in a transverse field. The analytic solutions and phase diagrams of this model are…
We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light…
This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory…