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Domb C., Lebowitz J.L. — Phase Transitions and Critical Phenomena (Vol. 19)
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Íàçâàíèå: Phase Transitions and Critical Phenomena (Vol. 19)Àâòîðû: Domb C., Lebowitz J.L. Àííîòàöèÿ: This series of publications was first planned by Domb and Green in 1970. During the previous decade the research literature on phase transitions and critical phenomena had grown rapidly and, because of the interdisciplinary nature of the field, it was scattered among physical, chemical, mathematical and other journals. Much of this literature was of ephemeral value, and was rapidly rendered obsolete. However, a body of established results had accumulated, and the aim was to produce articles that would present a coherent account of all that was definitely known about phase transitions and critical phenomena, and that could serve as a
ßçûê: Ðóáðèêà: Ôèçèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2001Êîëè÷åñòâî ñòðàíèö: 498Äîáàâëåíà â êàòàëîã: 19.03.2006Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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108 109 119 181 186 416 446 302 347 357 373 464 466 142 367 417 419 447 307 402 403 446 464 304 452 463 371 372 446—447 360 364—368 349 350 429 446—447 264 393 439 256 446 402 444 417 316 360 363 440 427 316 317 256 286 264 354 363 364 369—370 Absorbing subset 56—57 actin filaments 10 Algebraic decay 63 67 68 74 99 Aluminium foil, crumpled, fractal dimension 275—276 Anharmonicity of elastic terms 376 Anisotropy, cubic 430 431 433 Anisotropy, tethered membranes 375 Annihilation process 6 49—50 72 195 210 see Pair Random annihilating Annihilation-creation process 6 26—27 84 Annihilation-exclusion process 173 Annihilation-fusion process 206 Anticommutation relations 175 177 200 202 Anticorrelations 196—197 Antiferromagnetism 32 156 Antiperiodic boundary conditions 178 179 Approximation methods 5 see e.g. ASEP see Asymmetric simple exclusion process (ASEP) Asymmetric simple exclusion process (ASEP) on a ring 110—114 160 Asymmetric simple exclusion process (ASEP), applications 52 Asymmetric simple exclusion process (ASEP), boundary conditions 11 44 Asymmetric simple exclusion process (ASEP), empty interval probabilities 237—238 Asymmetric simple exclusion process (ASEP), exact solution 125—135 Asymmetric simple exclusion process (ASEP), finite size behaviour 111—114 Asymmetric simple exclusion process (ASEP), generalizations 159 Asymmetric simple exclusion process (ASEP), master equation 114 Asymmetric simple exclusion process (ASEP), nearest-neighbour jumps 43 Asymmetric simple exclusion process (ASEP), randomness 160 Asymmetric simple exclusion process (ASEP), self-duality 104—110 Asymmetric simple exclusion process (ASEP), self-enantiodromy 108—110 Asymmetric simple exclusion process (ASEP), shocks 12 117—123 Asymmetric simple exclusion process (ASEP), stationary distributions 117 Asymptotic behaviour, ASEP 112 113 Asymptotic behaviour, nonequilibrium systems 53—71 Asymptotic behaviour, particle systems 59—69 Asymptotic behaviour, scattering amplitude 101 Autocorrelation function 99 385 Band collapse 215 Baxterization 50 Bead and tether model 276—277 Bending rigidity, crumpling transition 276—277 Bending rigidity, entropic 258 Bending rigidity, flat phase 268 271 272 Bending rigidity, fluid membranes 261—262 265—267 Bending rigidity, self-avoiding membranes 356 Bending rigidity, spectrin in red blood cells 274 Bessel functions 64 98 121 169 170 Bethe ansatz equations (BAE) 40 110 111—112 Bethe ansatz methods, anisotropic Heisenberg chain 114—117 Bethe ansatz methods, asymmetric simple exclusion process (ASEP) 111 Bethe ansatz methods, coordinate 90 Bethe ansatz methods, correlations 51 99—100 Bethe ansatz methods, current fluctuation 158—159 Bethe ansatz methods, formalism 24 Bethe ansatz methods, history 34 Bethe ansatz methods, infinite system 114—117 Bethe ansatz methods, integrability 52 79 Bethe ansatz methods, polymers 220 223 Bethe ansatz methods, solution 35—41 84—88 Bethe ansatz methods, typical results 5—6 Bethe ansatz methods, wave function 97 99—100 101 Bethe wave function ( 86 101 111 166 175 Bethe, Hans 32 34 Bilinear property 212—213 Bilocal operator 365 397—399 Binding centre 372 Binomial coefficients 107 129 130 Biological systems, fluid membranes 257 Biological systems, growth 3 163—164 Biopolymerization 10—12 43 104 148 220—222 Blockage 160 Boltzmann weights 225 227 377 431 Borel methods 260 349 446 Boundary conditions and bulk state 125 Boundary conditions, antiperiodic 178 179 213 Boundary conditions, exclusion interaction 86 114—115 Boundary conditions, free fermion system 213 Boundary conditions, Glauber dynamics 213 Boundary conditions, Neumann 362 Boundary conditions, nonequilibrium systems 103 Boundary conditions, open 89 125—126 211—212 226 Boundary conditions, periodic 38—40 63 110—114 178 179 182 194 213 Boundary conditions, polymers 220 Boundary conditions, reflecting 66 67 104 105 111 Boundary conditions, two-particle 93 Boundary conditions, types 44 Boundary conditions, wave function 37 Boundary densities 96 151 Boundary effects, critical behaviour 361—363 Boundary effects, phase transitions 52 103 104 126 143—154 157 Boundary effects, relaxational behaviour 98 Boundary effects, reservoir-coupled systems 88—89 Boundary effects, shock distributions 120 Boundary fields 44 97—98 Boundary operators 360 363 Boundary terms, master equation 91 Bra-ket notation 24 295 454 Branching processes 47 150—151 152 172 Branching ratio 206 Branching-fusion process 184 185 Brownian motion 9 23 65 411 439 bubbles 431 Bulk, contact exponent 357—359 Bulk, correlator 362 Bulk, density 125—128 138 139 Bulk, dynamics, deterministic 136 160 Bulk, equation 66 Bulk, Hamiltonian 90 Bulk, hopping rate 145 Bulk, phases 126 Bulk, scheme O(N) system 425 Bulk, state, and boundary conditions 125 Burgers equation, lattice realization 104 Canham — Helfrich Hamiltonian 261—262 Canonical dimension 365 366 407 456 465 Canonical distributions 62 108 cells see Biological systems Characteristic function 321 361 Chemical annihilation 194 199 Chemical annihilation-creation reaction 6 chemical potential 156 373 412 413 414 421 423 428 457 Chemical reactions, diffusion limitation 6 194—197 222—223 Coagulation 47 Coalescence, shocks 47 117—123 150—151 152 Coexistence line 134 Combinatorial factor 420 Commutation relations 141 177 Commuting transfer matrices 31 39 Compact phase 256 259 Complex systems in nature 3—4 Complex systems, modelling 6—13 conditional probabilities 67 79 84—85 86—88 Configuration space 394 Confining tube 8 10 217 Conformal field theory 451 Conformal mapping of sectors 311—313 Connected components and molecules 319 320 Conservation laws 31 32 35 99 Conservation of probability 92—93 181 183 189 Contact exponent, bulk 357—359 Continuous and discrete time processes 13—16 28 30 Contraction, dipoles 293—297 300—301 352 353 360 382 462 Contraction, divergent 365 Contraction, interaction 383—384 Convection 388 Correlation/correlators and canonical distributions 108 Correlation/correlators and pair annihilation 195 Correlation/correlators and perturbations 99 Correlation/correlators and response function 383 394 Correlation/correlators, 316 Correlation/correlators, additive 313—314 Correlation/correlators, amplitude 143 Correlation/correlators, Bethe ansatz method 99—100 Correlation/correlators, calculation 197—198 209 214 Correlation/correlators, canonical dimension 456 Correlation/correlators, decoupling 222 Correlation/correlators, density 108 Correlation/correlators, derivation 452 Correlation/correlators, divergences 297 Correlation/correlators, driving effects 203 Correlation/correlators, energy-energy 257 408 Correlation/correlators, equal time 140 Correlation/correlators, equations of motion 164—165 Correlation/correlators, exponential decay 168 Correlation/correlators, higher order 96 164 Correlation/correlators, Laplace transformed 315—316 Correlation/correlators, large-scale/limit behaviour 88 199 456 Correlation/correlators, lower order 165 Correlation/correlators, multipoint 141 Correlation/correlators, polymers 315 412 Correlation/correlators, random force field 390—391 Correlation/correlators, static 377 Correlation/correlators, stationary 140—141 Correlation/correlators, three point 117 Correlation/correlators, time derivative 380 Correlation/correlators, time-delayed 58 59 141 Correlation/correlators, time-dependent 6 25 74 84 91 136 141 142—143 174 Correlation/correlators, two-point 117 140 141 166 Coulomb energy 283 285 380—381 Coulomb potential 283 Counterterms 298 299 341 382 383 Coupling, constant 302 342 366 435 Coupling, constant, canonical dimension 365 366 465 Coupling, constant, renormalization 354 382 420 447 Coupling, physical interpretation 368 Coupling, renormalized 301 302 393 Critical behaviour and nonleading terms 259 Critical behaviour, boundary effect 361—363 Critical behaviour, modelling 4 Critical behaviour, N-component spins 256 Critical behaviour, reaction-diffusion systems 70—71 Critical behaviour, renormalization group 5 Critical behaviour, tethered membranes 259 Critical dimensions, phase separators 364 Critical exponents 351 421 426 Critical points 369 370 see Critical theory 428 Crossover 66 116 197 199 218 305 407—408 Crumpled phase 265 275 Crumpled swollen phase 257—258 259 Crumpling transition 263 265—267 273 276—277 356 Cumulant function 204—205 Curie temperature 32 Current fluctuation, Bethe ansatz methods 158—159 Current maxima and minima 111 144 149—154 161 Current maximal 133—134 143 144 146 155 157 Current nonvanishing 59 Current stationary 66 104 Current-density relation and parallel updating 137—138 Current-density relation and phase diagram 144 153 Current-density relation, exact results 148 150 Current-density relation, point of inflection 125 Current-density relation, stationary 111 Current-density relation, traffic models 155—156 157 Decoagulation 47 see Decoupling, correlators 222—223 Decoupling, equations of motion 164—167 Defects, in polymers 8 9 Deformation, energy 268 Deformation, matrix 267—268 278 Deformed harmonic oscillator algebra 97 Density, asymptotic behaviour 53 Density, correlation function 93 Density, decay 72 141 171 195 198 205 Density, expectation value 168 Density, finite 101 117 Density, fluctuations 167—169 203—208 Density, functional theories 230 Density, matrix renormalization method (DMRG) 71 Density, nonconstant 161 Density, perturbation, local 59 Density, profile, constituent profiles 140 143 Density, profile, diffusion limited pair annihilation (DLPA) 209 Density, profile, exact results 100 128—134 132 Density, profile, field induced oscillations 167—169 Density, profile, Gaussian distribution 67 Density, profile, lattice derivative 130—131 Density, profile, relaxation 97 Density, profile, shape 134 143 Density, profile, single particle 64 Density, profile, stationary 126 128 148—149 Density, profile, TASEP 139 149 Density, profile, thermodynamic limit 131—134 Density, profile, time evolution 62 99 117—118 122 Density, relaxation 59—61 97—99 165—166 167 169 185 Density, stationary 137 168 Density, time dependent 208 Detailed balance 57—59 62 103 104—105 110 Determinant representation 158 159 Diffusion of reconstituting dimers 101 Diffusion, coefficient 23 82—83 124 148 169 Diffusion, collective 116 Diffusion, constant 60 116 149 197 Diffusion, discrete—time dynamics 97 Diffusion, in inhomogeneous media 42 Diffusion, limitation 4 Diffusion, master equation 63 Diffusion, perturbation 124 Diffusion, propagator, probability conserving 314 Diffusion, shocks 117—123 Diffusion, tracer 44—45 Diffusion-limited annihilation 49—50 195 Diffusion-limited branching-fusion 74 167 Diffusion-limited chemical reactions 6 194—197 222—223 Diffusion-limited fusion 163 164 168—169 181 Diffusion-limited pair annihilation (DLPA) 49—50 193—210 Diffusion-limited pair annihilation (DLPA) and DLFPA 77 Diffusion-limited pair annihilation (DLPA) and Glauber dynamics 74 163 Diffusion-limited pair annihilation (DLPA), density 205 209 Diffusion-limited pair annihilation (DLPA), dynamics 193—211 Diffusion-limited pair annihilation (DLPA), Hamiltonian 73 181
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