Ground States, Energy Landscape, and Low-Temperature Dynamics of ± J Spin Glasses
Ground States, Energy Landscape, and Low-Temperature Dynamics of ± J Spin Glasses
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
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .
