Related papers: Spin Systems and Computational Complexity
Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of complex systems. After a brief review of basic spin glass concepts, their use in areas such as computer science, biology, and other…
Spin glasses are magnetic systems exhibiting both quenched disorder and frustration, and have often been cited as examples of `complex systems.' In this talk I review some of the basic notions of spin glass physics, and discuss how some of…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
Some questions concerning the calculation of the number of ``physical'' (metastable) states or complexity of the spherical $p$-spin spin glass model are reviewed and examined further. Particular attention is focused on the general…
An introduction and overview is given of the theory of spin glasses and its application.
The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…
The aim of this work is to prove that it is possible to realise an optical system which produces as output a light intensity that can be expressed in the same mathematical form of the spin glass Hamiltonian. The optical system under study…
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…
We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method,…
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is…
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…
In this talk I present some of the recent theoretical results that have been obtained on glassy systems like spin glasses or structural glasses. The physical principles at the basis of the theory are explained in a simple language (without…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
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…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
Non-deterministic polynomial-time (NP) problems are ubiquitous in almost every field of study. Recently, all-optical approaches have been explored for solving classic NP problems based on the spin-glass Ising Hamiltonian. However, obtaining…
The p-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly…
Recent studies on the spin and the chirality orderings of the three-dimensional Heisenberg spin glass and related systems are reviewed with particular emphasis on the possible spin-chirality decoupling phenomena. Chirality scenario of real…
In this chapter, I review the main methods and techniques of complex systems science. As a first step, I distinguish among the broad patterns which recur across complex systems, the topics complex systems science commonly studies, the tools…
In this paper I will consider many of the various definitions of the overlap and of its probability distribution that have been introduced in the literature starting from the original papers of Edwards and Anderson; I will present also some…