Spin Glasses. Still Complex After All These Years?

Stein, D. L.

doi:10.1002/chin.200441226

Cited by 6 publications

(7 citation statements)

References 52 publications

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“…We emphasize that we will not attempt to provide a comprehensive or even an extensive answer to this question, which remains largely open, but will only focus on some of the insights that our analysis of the spin glass problem may have uncovered. (A similar discussion appears also in [127]. )…”

Section: The Statistical Mechanics Of Homogeneous Vs Disordered Systemssupporting

confidence: 72%

Ordering and broken symmetry in short-ranged spin glasses

Newman

Stein

2003

J. Phys.: Condens. Matter

101

185

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In this topical review we discuss the nature of the low-temperature phase in both infiniteranged and short-ranged spin glasses. We analyze the meaning of pure states in spin glasses, and distinguish between physical, or "observable", states and (probably) unphysical, "invisible" states. We review replica symmetry breaking, and describe what it would mean in shortranged spin glasses. We introduce the notion of thermodynamic chaos, which leads to the metastate construct. We apply these tools to short-ranged spin glasses, and conclude that replica symmetry breaking, in any form, cannot describe the low-temperature spin glass phase in any finite dimension. We then discuss the remaining possible scenarios that could describe the low-temperature phase, and the differences they exhibit in some of their physical properties -in particular, the interfaces that separate them. We also present rigorous results on metastable states and discuss their connection to thermodynamic states. Finally, we discuss some of the differences between the statistical mechanics of homogeneous systems and those with quenched disorder and frustration.

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Section: The Statistical Mechanics Of Homogeneous Vs Disordered Systemssupporting

confidence: 72%

Ordering and broken symmetry in short-ranged spin glasses

Newman

Stein

2003

J. Phys.: Condens. Matter

101

185

View full text Add to dashboard Cite

show abstract

“…Widely explored experiments give us more and more information about magnetic properties of different kinds of material (spin-glass, paramagnetic, ferromagnetic etc.) molecules [2,8,13,17]. The result of experiments based on, e.g., Raman and EDX spectra [6,10,11] are agreed with theoretical analysis what confirm correctness of the models for supplementary investigations also theoretic.…”

Section: Introductionsupporting

confidence: 80%

“…Such operations on gates are essential for quantum computing also because of the quantum physics phenomena reversibility [16,20,21]. For theoretical physics quantum computing can be seen as a new challenge and also a new source of stimuli aims and paradigms how to deal with one of the most basic problems for contemporary science (physics) [17,19]. The big question is: how to resolve mysteries paradoxes and quite evident incompleteness of the most basic powerful and fascinating theory in physics, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Consideration of analogies between magnetic and quantum notices for molecular network

2018

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Abstract. Magnetic properties of spin glass materials [9,13] are close to quantum interpretation in their nature description [17]. Therefore, we can look for possible kinds of analogies in process of defining theoretic and practice conventions, rules and applications of the specific characteristics in elaboration quantum calculation strategies. We have not investigated possibilities to create directly quantum calculation units and practice calculation structures like qubits, registers, gates etc. [4,18], but dealing with spin and quantum definitions and descriptions we can try to involve these notices from different domains. Such a pragmatic approach only intuitively gives chances to create the transition theory and implement it even partially. Obviously, almost all of us have heard about quantum factorization, cryptography or teleportation but it is obtained as a result of exploration casually selected quantum properties and adapting them to mathematic problems. In our approach, we carefully investigate involutions among spin and quantum nature looking at possible implementation in molecular network.

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“…Here are what one might call the "canonical complex systems", the particular systems, natural, artificial and fictional, which complex systems science has traditionally and habitually sought to understand. Here we find networks (Wuchty, Ravasz and Barabási, this volume), turbulence [13], physio-chemical pattern formation and biological morphogenesis [14,15], genetic algorithms [16,17], evolutionary dynamics [18,19], spin glasses [20,21], neuronal networks (see Part III, 4, this book), the immune system (see Part III, 5, this book), social insects, ant-like robotic systems, the evolution of cooperation, evolutionary economics, etc. 1 These topics all fall within our initial definition of "complexity", though whether they are studied together because of deep connections, or because of historical accidents and tradition, is a difficult question.…”

Section: Introductionmentioning

confidence: 99%

Methods and Techniques of Complex Systems Science: An Overview

Shalizi

Topics in Biomedical Engineering International Book Series

156

102

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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 employed, and the foundational science of complex systems. The focus of this chapter is overwhelmingly on the third heading, that of tools. These in turn divide, roughly, into tools for analyzing data, tools for constructing and evaluating models, and tools for measuring complexity. I discuss the principles of statistical learning and model selection; time series analysis; cellular automata; agent-based models; the evaluation of complex-systems models; information theory; and ways of measuring complexity. Throughout, I give only rough outlines of techniques, so that readers, confronted with new problems, will have a sense of which ones might be suitable, and which ones definitely are not.

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Spin Glasses. Still Complex After All These Years?

Cited by 6 publications

References 52 publications

Ordering and broken symmetry in short-ranged spin glasses

Ordering and broken symmetry in short-ranged spin glasses

Consideration of analogies between magnetic and quantum notices for molecular network

Methods and Techniques of Complex Systems Science: An Overview

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