Spin Glasses

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Spin Glasses / Erwin Bolthausen, Anton Bovier, J.-M Morel Cachan, F. Takens Groningen, B. Teissier Paris

資料種別:

電子ブック

出版情報:

SpringerLink Books - AutoHoldings
Springer Berlin Heidelberg, 2007

著者名:

ISBN:

9783540409021 [3540409025]
9786610745357 [6610745358]

書誌ID:

OB00589159

子書誌情報

フルテキスト

所蔵情報

書誌詳細

言語:

英語

目次情報:

Random Media and Spin Glasses: An Introduction into Some Mathematical Results and Problems / Erwin Bolthausen

Introduction / 1：

The Basic Mathematical Models / 2：

The Sherrington-Kirkpatrick Model / 3：

Basic Properties of the SK-Model / 3.1：

The Replica Computation / 3.2：

The Parisi Ansatz / 3.3：

Mathematically Rigorous Results for the SK-Model / 4：

Guerra's Interpolation Method / 4.1：

Mathematical Variants of the Cavity Method / 4.2：

The Random Energy Models / 5：

The REM / 5.1：

The Generalized Random Energy Model / 5.2：

The Aizenman-Sims-Starr Proof of Guerra's Bound of the SK Free Energy / 5.3：

Some Open Problems: Ultrametricity and Chaos / 6：

Other Models: Some Comments about the Perceptron / 7：

Dynamic Problems and Aging / 8：

References

Spin Glasses: A Perspective / David Sherrington

Random Magnetic Alloys

More Details / 2.1：

Discontinuous Transitions

Beyond Magnetic Alloys

Complex Many-Body Problems

Dynamics

Examples

Conclusion

Acknowledgements

Mean Field Models for Spin Glasses: Some Obnoxious Problems / Michel Talagrand

Guerra's Replica-Symmetric Bound

Guerra's Broken Replica-Symmetry Bound

The Ultrametricity Conjecture

The Chaos Problem

Much Ado about Derrida's GREM / Anton Bovier ; Irina Kurkova

History of the Models / 1.1：

Geometry of Gibbs Measures / 1.2：

Point Process of Extremes / 1.3：

Organisation of the Paper / 1.4：

Convergent Point Processes Associated to the GREM

GREM: Detailed Analysis

Fluctuations of the Partition Function

Gibbs Measure: Approach via Ruelle's Probability Cascades

Distribution of the Overlaps

Ghirlanda-Guerra Identities / 3.4：

Empirical Distance Distribution Function [Kappa subscript beta] / 3.5：

CREM: Implicit Approach

Maximum of the Hamiltonian. Limit of the Free Energy

Two-Replicas Ultrametric Distance Distribution Function

Marginals of [Kappa subscript beta] in Terms of Ruelle's Probability Cascades / 4.3：

Genealogies and Neveu's Branching Process

Problems with the Explicit Description of Limiting Gibbs Measures

Genealogical Map of a Flow of Probability Measures

Coalescent Associated with a Flow of Probability Measures

Finite N Setting for the CREM / 5.4：

Genealogy of a Continuous State Branching Process / 5.5：

Main Result / 5.6：

Coalescence and Ghirlanda-Guerra identities / 5.7：

Dynamics for Spherical Models of Spin-Glass and Aging / Alice Guionnet

Spherical Sherrington-Kirkpatrick Model

Spherical p-spins Model

Future problems

Local vs. Global Variables for Spin Glasses / Charles M. Newman ; Daniel L. Stein

Local Variables and Thermodynamic Limits

Nearest-Neighbor Ising Ferromagnets

Finite-Range and Infinite-Range Spin Glasses

A New Global Order Parameter for Spin Glasses?

What are Metastates, Anyway?

Short-Range Spin Glasses: Results and Speculations

The Trinity of Scenarios

Heuristic Description

Description via the Metastate / 2.2：

Replica Symmetry Breaking for Short-Range Models

Wild Possibilities

Phase Transition Without Broken Spin-Flip Symmetry

Highly Chaotic Temperature Dependence

Index

Random Media and Spin Glasses: An Introduction into Some Mathematical Results and Problems / Erwin Bolthausen

Introduction / 1：

The Basic Mathematical Models / 2：

The Sherrington-Kirkpatrick Model / 3：

Basic Properties of the SK-Model / 3.1：

The Replica Computation / 3.2：

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