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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 PerspectiveАвторы: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 380Добавлена в каталог: 14.05.2008Операции: Положить на полку |
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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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