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Bovier A., Gill R. (Ed), Ripley B.D. (Ed) — Statistical Mechanics of Disordered Systems: A Mathematical Perspective
Bovier A., Gill R. (Ed), Ripley B.D. (Ed) — Statistical Mechanics of Disordered Systems: A Mathematical Perspective



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Название: Statistical Mechanics of Disordered Systems: A Mathematical Perspective

Авторы: Bovier A., Gill R. (Ed), Ripley B.D. (Ed)

Аннотация:

Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 380

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Aizenman, M.      72 100 111 118 167 230
Amit, D.J.      271
Average annealed      98
Average quenched      98
Bassalygo, L.A.      106
Bauke, H.      287
Baxter, R.J.      48
Ben Arous, G.      170
Berretti, A.      107
Binomial coefficient, asymptotics      41
Bodineau,Th.      72
Bogachev, L.      170
Borgs, Ch.      286
Branching process, Neveu’s      231
Brascamp — Lieb inequalities      274
Bricmont, J.      111 125
Brydges, D.      81 112
canonical ensemble      19
Canonical partition function      19
Cavity method      271 280
Central limit theorem, functional      253
Chaining      115 258
Chayes, J.T.      286
Chebychev inequality      259
Cluster      77
Cluster expansion      77
Comets, F.      167 250
Comparison lemma, Gaussian      197 218 228
Concave hull      190
Concentration of measure      113 219 264
Conditional distribution      56 101
Conditional distribution, regular      56
Conditional expectation      56
Contour models      127
Contucci, P.      182
Convexity      7 45
Convexity, local      266
Cramer entropy      41
CREM      195
Curie — Weiss model      39 161
Curie, P.      39
Cylinder function      53
Derrida, B.      165 186 196
Dimensional reduction      112
Disordered system      98
Distance, Hamming      163
Distance, lexicographic      164
Distance, ultrametric      164
Distribution, micro-canonical      10
DLR equations      57
Dobrushin states      72
Dobrushin, R.L.      51 62 64 72 81 106
Edwards — Anderson model      109
Empirical distance distribution      196 202
Ensemble, Canonical      19
Ensemble, equivalence of      21
Ensemble, micro-canonical      13
Enthalpy      7
entropy      5 15
Entropy of a measure      18
Entropy, Cramer      41
Entropy, relative      18
Equation of state, Van der Waals      29
Ergodic theorem      121
Expansion, cluster      77
Expansion, high-temperature      73
Expansion, low-temperature      88
Expansion, Mayer      77
Extremal process      187 287
Extreme value statistics      166
Extreme value theory      220
ferromagnetism      35
Figotin, A.L.      249
Fisher, D.      113
FKG inequalities      68 118
Flow of probability measures      207
Fluctuations of REM partition function      169
Free energy in SK model      218 237
Free energy of spin system      35
Free energy, annealed      98
Free energy, Gibbs      7
Free energy, GREM      192
Free energy, Helmholtz      7
Free energy, quenched      98
Frohlich, J.      107 113
Frustration      110
Gallavotti, G.      72 81
Gardner, E.      196
Gaussian, comparison lemma      197 228
Gaussian, process      163
Gayrard, V.      257
genealogy      231
Generalized random energy model      186
Generating functions      121
Gentz, B.      258
Georgii, H.-O.      109
Ghirlanda — Guerra relations      182
Ghirlanda — Guerra relations, extended      239
Ghirlanda — Guerra relations, SK model      238
Ghirlanda, S.      182
Gibbs measure      19
Gibbs measure, infinite-volume      52 57
Gibbs measure, random      99 100
Gibbs measure, random, covariant      119
Gibbs measure, weak      57
Gibbs specification random      100
Gibbs state, extremal      108
Gielis, G.      106
GREM      186 232
GREM, free energy      192
GREM, partition function      192
Griffiths, R.B.      64 100
Ground-state      89 110 126
Guerra, F.      163 182 218 235
Guerra’s bound      235
Gutfreund, H.      271
Hebb, D.      248
Hebb’s rule      248
Higuchi, Y.      72
Holder’s Inequality      124
Hopfield Hamiltonian      249
Hopfield model      162 247
Hopfield, J.J.      247
Ideal gas      9
Imbrie, J.Z.      107 112
Imry—Ma argument      111
Inclusion-Exclusion Principle      288
Inequality, Bonferroni      288
Inequality, Brascamp — Lieb      274
Inequality, Chebychev      259
Inequality, concentration      264
Inequality, FKG      68
Inequality, Marcinkiewicz — Zygmund      259
Inequality, Paley — Zygmund      223
Infinite volume      51
Integration by parts, Gaussian      182
Integration by parts, multivariate      197
Interaction      54
Interaction, absolutely summable      54
Interaction, continuous      54
Interaction, nearest-neighbor      34
Interaction, random      99
Interaction, regular      54
Internal energy      6
Interpolation, Gaussian      218
Ising model      35
Ising model, dilute      107
Ising model, one dimensional      37
Ising model, random field      111
Ising, E.      34
Isotherm      45
Joint measure      101
Kahane, J.-P.      197
Kirkpatrick, S.      163 218
Klein, A.      107
Koch, H.      257
Kotecky — Preiss criterion      77
Kotecky, R.      81
Kulske, Ch.      104 106
Kupiainen, A.      111 125
Kurkova, I.      169 186
Lanford, O.E.      51
Large deviation      250
Large deviation, principle      42 250
Lattice gas      33
Lattice gas, ideal      17
Lattice gas, Ising      34
Lebowitz, J.      167
Legendre transform      6 20
Lieb, E.H.      8 48
Lindeberg condition      170
Lipschitz continuous      113
Local specification      55
Local specification, Gibbs      56
Local specification, random      99 100
Lowe, M.      169 258
Lumping      243
Lumps      244 253 264
Maes, Ch.      106
Magnetic field      35
Magnetisation      35
Marcinkiewicz — Zygmund inequality      259
Martingale-difference sequence      123
Mason, D.M.      258
Masooman, S.      107
Mayer expansion      77
Mean-field models      40 161
Mean-field models, disordered      161
Memory, autoassociative      248
Memory, capacity      249
Mertens, St.      285 287
Metastate      99 178 253
Metastate, Aizenman — Wehr      103 256 279
Metastate, empirical      103
Micro-canonical ensemble      13
Micro-canonical partition function      14
Miracle-Sole, S.      72 81
Molchanov, S.      170
Multi-index      77
Neural network      247
Neveu, J.      167 178
Newman, Ch.      100
Non-convexity      45
Number partitioning      285
Onsager, L.      47
Paley — Zygmund inequality      223
Parisi solution      231 235
Parisi, G.      112 163 235
Partition function      14
Partition function, canonical      19
Partition function, GREM      192
Partition function, micro-canonical      14
Pastur, L.A.      249 272
Peierls argument      107
Peierls, R.      64
Phase separation      45
Phase transition      7
Phase transition, first order      7
Phase transition, higher order      7
Phase transition, liquid—vapour      29
Piasko,J.      257
Picco, P.      257
Pirogov — Sinai theory      89
Pirogov, S.A.      89
Pittel, J.      286
Point process, Poisson      169
Poisson cascade      187
Poisson process of extremes      171 287
Poisson — Dirichlet process      206
Polymer      74
Polymer, connected      74
Polymer, high-temperature      74
Polymer, model, abstract      76
Polymer, representation      75
Potential, chemical      5
Preiss, D.      81
Pressure      5
Presutti, E.      31
Probability measure, flow of      207
Pure state      178
Quasi-local function      53
quenched      98
Random energy model (REM)      165 287
random matrix      260
Random matrix, Marchenko — Pastur      260
Random matrix, sample covariance      260
Random model      98
Random overlap structure      230
Random process, Gaussian      163
Random subsequences      100
Random-field Ising model      111
Regular conditional distribution      56
Regular interaction, random      99
Renormalization group      125
Renormalization group, transformation      127
Replica, method      227
Replica, symmetric solution      271
Replica, symmetry breaking      228
Ruelle, D.      51 167
Second moment method      167 220
Second moment method, truncated      167
Self-averaging      113
Shcherbina, M.      257
Sherrington — Kirkpatrick (SK) model      162
Sherrington, D.      163 218
Sims, R.      230
Sinai, Ya.G.      89
Slepian, D.      221
Slepian’s lemma      220
Sokal, A.      82
Sompolinski, H.      271
Sourlas, N.      112
Spencer, T.      113
Spin, configuration      34
Spin, system      35
Spin, variable      34
Spin-glass      109 163
Starr, S.L.      230
Stein, D.      100
storage capacity      258
Subadditivity      36 219
Tail sigma-algebra      53
Talagrand, M.      113 163 167 237 264 272
Talagrand’s theorem      237
Taylor expansion      265
Temperature      5 16
Thermodynamic limit      21
Thermodynamic potentials      6
Thermodynamic variables      5
Thermodynamic variables, extensive      5
Thermodynamic variables, intensive      5
Thermodynamics      5
Thermodynamics, first law of      5
Tirozzi, B.      257
Toninelli, F.-L.      163 218 237
Topology, product      50
Transfer matrix      38
Transformation, Hubbard — Stratonovich      46 250
Translation-covariant state      118
Ueltschi, D.      82
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