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Computational Complexity and Statistical Physics$
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Allon Percus, Gabriel Istrate, and Cristopher Moore

Print publication date: 2005

Print ISBN-13: 9780195177374

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195177374.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 17 October 2021

Ground States, Energy Landscape, and Low-Temperature Dynamics of ± J Spin Glasses

Ground States, Energy Landscape, and Low-Temperature Dynamics of ± J Spin Glasses

Chapter 6 Ground States, Energy Landscape, and Low-Temperature Dynamics of ± J Spin Glasses
Computational Complexity and Statistical Physics

Sigismund Kobe

Jarek Krawczyk

Oxford University Press

The previous three chapters have focused on the analysis of computational problems using methods from statistical physics. This chapter largely takes the reverse approach. We turn to a problem from the physics literature, the spin glass, and use the branch-and-bound method from combinatorial optimization to analyze its energy landscape. The spin glass model is a prototype that combines questions of computational complexity from the mathematical point of view and of glassy behavior from the physical one. In general, the problem of finding the ground state, or minimal energy configuration, of such model systems belongs to the class of NP-hard tasks. The spin glass is defined using the language of the Ising model, the fundamental description of magnetism at the level of statistical mechanics. The Ising model contains a set of n spins, or binary variables si, each of which can take on the value up (si = 1) or down (si= 1).

Keywords:   complete algorithms, degeneracy, energy barrier, ferromagnetic, glassy behavior, mirror states, plaquette, saddles, time complexity, valleys

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