Statistical Mechanics of Disordered Systems : A Mathematical Perspective.
 Publication:
 Cambridge : Cambridge University Press, 2006.
 Format/Description:
 Book
1 online resource (328 pages)  Series:
 Cambridge Series in Statistical and Probabilistic Mathematics
Cambridge Series in Statistical and Probabilistic Mathematics ; v.18  Status/Location:

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 Other records:
 Subjects:
 Statistical mechanics.
 Form/Genre:
 Electronic books.
 Summary:
 A selfcontained graduatelevel introduction to the statistical mechanics of disordered systems.
 Contents:
 Cover
Halftitle
Seriestitle
Title
Copyright
Dedication
Contents
Preface
Nomenclature
Part I Statistical mechanics
1 Introduction
1.1 Thermodynamics
2 Principles of statistical mechanics
2.1 The ideal gas in one dimension
2.2 The microcanonical ensemble
2.3 The canonical ensemble and the Gibbs measure
2.4 Nonideal gases in the canonical ensemble
2.5 Existence of the thermodynamic limit
2.6 The liquidvapour transition and the van der Waals gas
2.7 The grand canonical ensemble
3 Lattice gases and spin systems
3.1 Lattice gases
3.2 Spin systems
3.3 Subadditivity and the existence of the free energy
3.4 The onedimensional Ising model
3.5 The CurieWeiss model
4 The Gibbsian formalism for lattice spin systems
4.1 Spin systems and Gibbs measures
4.2 Regular interactions
4.2.1 Some topological background
4.2.2 Local specifications and Gibbs measures
4.3 Structure of Gibbs measures: phase transitions
4.3.1 Dobrushin's uniqueness criterion
4.3.2 The Peierls argument
4.3.3 The FKG inequalities and monotonicity
5 Cluster expansions
5.1 Hightemperature expansions
5.2 Polymer models: the DobrushinKoteckĀ“yPreiss criterion
5.3 Convergence of the hightemperature expansion
5.4 Lowtemperature expansions
5.4.1 The Ising model at zero field
5.4.2 Groundstates and contours
Part II Disordered systems: lattice models
6 Gibbsian formalism and metastates
6.1 Introduction
6.2 Random Gibbs measures and metastates
6.3 Remarks on uniqueness conditions
6.4 Phase transitions
6.5 The EdwardsAnderson model
7 The randomfield Ising model
7.1 The ImryMa argument
7.2 Absence of phase transitions: the AizenmanWehr method
7.2.1 Translationcovariant states
7.2.2 Order parameters and generating functions.
7.3 The BricmontKupiainen renormalization group
7.3.1 Renormalization group and contour models
7.3.2 The groundstates
7.3.3 The Gibbs states at finite temperature
Part III Disordered systems: meanfield models
8 Disordered meanfield models
9 The random energy model
9.1 Groundstate energy and free energy
9.2 Fluctuations and limit theorems
9.3 The Gibbs measure
9.4 The replica overlap
9.5 Multioverlaps and GhirlandaGuerra relations
10 Derrida's generalized random energy models
10.1 The standard GREM and Poisson cascades
10.1.1 Poisson cascades and extremal processes
10.1.2 Convergence of the partition function
10.1.3 The Gibbs measures
10.2 Models with continuous hierarchies: the CREM
10.2.1 Free energy
10.2.2 The empirical distance distribution
10.2.3 Multioverlap distributions
10.3 Continuous state branching and coalescent processes
10.3.1 Genealogy of flows of probability measures
10.3.2 Coalescent processes
10.3.3 Finite N setting for the CREM
10.3.4 Neveu's continuous state branching process
10.3.5 Coalescence and GhirlandaGuerra identities
11 The SK models and the Parisi solution
11.1 The existence of the free energy
11.2 2nd moment methods in the SK model
11.2.1 Classical estimates on extremes
11.3 The Parisi solution and Guerra's bounds
11.3.1 Application of a comparison lemma
11.3.2 Computations with the GREM
11.3.3 Talagrand's theorem
11.4 The GhirlandaGuerra relations in the SK models
11.5 Applications in the pspin SK model
12 Hopfield models
12.1 Origins of the model
12.2 Basic ideas: finite M
12.3 Growing M
12.3.1 Fluctuations of Phi
12.3.2 Logarithmic equivalence of lumpweights
12.4 The replica symmetric solution
12.4.1 Local convexity
12.4.2 The cavity method 1.
12.4.3 BrascampLieb inequalities
12.4.4 The local mean field
12.4.5 Gibbs measures and metastates
12.4.6 The cavity method 2
13 The number partitioning problem
13.1 Number partitioning as a spinglass problem
13.2 An extreme value theorem
13.3 Application to number partitioning
References
Index.  Notes:
 Description based on publisher supplied metadata and other sources.
 Contributor:
 Gill, R.
Ripley, Brian D.
Ross, S.
Silverman, B.W.
Stein, M.  Other format:
 Print version: Bovier, Anton Statistical Mechanics of Disordered Systems
 ISBN:
 9780511167690
9780521849913  OCLC:
 173610031