Related papers: Spin Systems and Computational Complexity
In this work a short overview of the development of spin glass theories, mainly long and short range Ising models, are presented.
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
Numerical simulations on Ising Spin Glasses show that spin glass transitions do not obey the usual universality rules which hold at canonical second order transitions. On the other hand the dynamics at the approach to the transition appear…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formulating problems and results in quantum spin systems is…
This paper characterizes the annealed complexity of bipartite spherical spin glasses, both pure and mixed. This means we give exact variational formulas for the asymptotics of the expected numbers of critical points and of local minima.…
Computing the ground state of Ising spin-glass models with p-spin interactions is, in general, an NP-hard problem. In this work we show that unlike in the case of the standard Ising spin glass with two-spin interactions, computing ground…
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…
In talk I will review the theoretical results that have been obtained for spin glasses, paying a particular attention to finite dimensional spin glasses. I will concentrate my attention on the formulation of the mean field approach and on…
Spin glass systems as lattices of disordered magnets with random interactions have important implications within the theory of magnetization and applications to a wide-range of hard combinatorial optimization problems. Nevertheless, despite…
We discuss the underlying connections among the thermodynamic properties of short-ranged spin glasses, their behavior in large finite volumes, and the interfaces that separate different pure states, and also ground states and low-lying…
In these notes the main theoretical concepts and techniques in the field of mean-field spin-glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is…
One may define a complex system as a system in which phenomena emerge as a consequence of multiscale interaction among the system's components and their environments. The field of Complex Systems is the study of such systems--usually…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
This note is an informal presentation of spin glasses and of the Parisi formula. We also discuss some models for which the Parisi formula is not well-understood, and some partial progress that relies upon a connection with partial…
We give an overview of numerical and experimental estimates of critical exponents in Spin Glasses. We find that the evidence for a breakdown of universality of exponents in these systems is very strong.
We review recent numerical progress in the study of finite dimensional strongly disordered magnetic systems like spin glasses and random field systems. In particular we report in some details results for the critical properties and the…
A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for…
We present a brief review on information processing, computing and inference via quantum fluctuation, and clarify the relationship between the probabilistic information processing and theory of quantum spin glasses through the analysis of…