Are Spin Glasses Complex Systems?

Author(s):  
Daniel L. Stein ◽  
Charles M. Newman

This chapter considers how spin glass science fits into the larger area of complexity studies. It discusses three landmark papers in the field of complexity, by Warren Weaver, Herb Simon, and Phil Anderson, respectively, and examines how the ideas they introduced might relate to the current understanding of spin glasses. It also takes a brief look at recent developments, in particular various proposals for measures of complexity, and considers how they might illuminate some features of spin glasses. It concludes by asking whether spin glasses can still be thought of as “complex systems,” and in so doing introduces a proposal for a kind of “new complexity” as it relates to spin glasses.

Author(s):  
Sigismund Kobe ◽  
Jarek Krawczyk

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).


1996 ◽  
Vol 07 (03) ◽  
pp. 345-353 ◽  
Author(s):  
HIKARU KAWAMURA

The results of the recent numerical simulations on vector spin glasses are presented. Numerical evidence of the novel chiral-glass state, accompanied with broken spin-reflection symmetry with preserving spin-rotation symmetry, is presented. Implication to experiments on spin-glass transitions is discussed.


2009 ◽  
Vol 21 (44) ◽  
pp. 4418-4441 ◽  
Author(s):  
Christoph Ulbricht ◽  
Beatrice Beyer ◽  
Christian Friebe ◽  
Andreas Winter ◽  
Ulrich S. Schubert

Author(s):  
G. Mossi ◽  
A. Scardicchio

By considering the quantum dynamics of a transverse-field Ising spin glass on the Bethe lattice, we find the existence of a many-body localized (MBL) region at small transverse field and low temperature. The region is located within the thermodynamic spin glass phase. Accordingly, we conjecture that quantum dynamics inside the glassy region is split into a small MBL region and a large delocalized (but not necessarily ergodic) region. This has implications for the analysis of the performance of quantum adiabatic algorithms. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.


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