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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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Glauber dynamics, zero temperature 163 193 206—207 213 264 Global rescaling, and equations of motion 305—307 Global symmetries, typical results 5—6 Grand canonical distribution 62 80 105 108 123 grand canonical ensemble 457 458 graphite 256 274 Graphite oxide 275 Gravitational field 104 Green function, derivation 459—461 Gregorshin theorem 54 Ground state energy 439 Hamiltonian, anisotropic transverse XY model 6 Hamiltonian, Canham — Helfrich 261—262 Hamiltonian, counterterms 298 299 Hamiltonian, diffusion-limited pair annihilation 73 Hamiltonian, driven and undriven systems 197 Hamiltonian, effective 269 270 279 436 Hamiltonian, equivalent 72 Hamiltonian, exclusion process 41—45 Hamiltonian, free energy 279 Hamiltonian, free fermion approach 178 180 189 194 Hamiltonian, free, integration by parts 306—307 Hamiltonian, Heisenberg 34—35 165 Hamiltonian, integral counterterms 298 Hamiltonian, membrane 278 Hamiltonian, modifed 297 Hamiltonian, nonstochastic 178—180 Hamiltonian, quantum spin model 5 33—34 Hamiltonian, renormalized 341 Hamiltonian, rescaled 436 Hamiltonian, static 377 Hamiltonian, stochastic 104 178—180 Hamiltonian, trial Gaussian 442—444 Hamiltonian, two-membrane model 358 Hard core, constraint 84 Hard core, interaction 79 96 103—104 Hard core, repulsion (site exclusion) 149—150 155 194 363 Harris criterion 433 434 Hartree — Fock approximation 442 443 Hecke algebra 50 63 68 188 211 213 Heisenberg fixed point 365 369 404 432 433 Heisenberg quantum chain, anisotropic 11 34—35 43 114—117 165 175 Heisenberg quantum chain, Hamiltonian 34—35 43 83 163 165 216 Heisenberg quantum chain, integrability 35 101 220 Heisenberg quantum chain, isotropic 111 163 216 Heisenberg quantum chain, properties 104 Heisenberg quantum chain, representation 23 33—35 Heisenberg quantum chain, stationary states 80 Heisenberg quantum chain, SU(2) symmetry 35 Heisenberg quantum chain, wave function 97 Heisenberg quantum chain, zero-field 43 Heisenberg quantum ferromagnet 6 10 34—35 41—42 89 Heisenberg, Paul 33 Helmholtz fluctuation theory 230 Hepp sectors 318 323 325—326 Hermitian, symmetric Hamiltonian 58 Hexatic membranes 264—265 High-density phase 132 133 138 139 140 142 145 146 172 High-temperature expansion, Ising model 257 408 431 High-temperature expansion, O(N) model 260 409—412 421 Holder’s Inequality 362 Homogenous factorized transformations 179 Hopf — Cole transformation 158 Hopping, asymmetry 104 183 197 203 212 Hopping, biased 66 Hopping, matrices 42 43 50 91 110 158 220 Hopping, nearest neighbour 84 85 Hopping, rate 9 19 27 57 103 145 Hopping, time 217 Hydrodynamic divergenceless flow 388 Hydrodynamic interaction 387 Hydrodynamic limit 62 124—125 Hydrodynamics, Zimm model 259 385—388 Hypergeometric function 238 Impurity-like interactions 463—464 Infinite membranes 417 418 456 Infinite systems and dynamical scaling 63—65 Infinite systems, Betheansatz 114—117 Infinite systems, density relaxation 98—99 Infinite systems, exponential decay 65 Infinite systems, hard-core interaction 103—104 Infinite systems, late time behaviour 159 Infinite time limit 53—54 Infinite volume limit 63 64 Infrared (IR), convergence 285 299 Infrared (IR), cutoff 272 321 419 Infrared (IR), divergences 280 282 284 Infrared (IR), finite observable 281 366—367 Infrared (IR), fixed point 305 354 357 358 368 369—370 426 446 457 464 466 Initial conditions, random 202 203 Injection rate, overfeeding 135 Instanton methods 260 434 435—439 441—442 443 Integrability and matrix representation 50 101 Integrability, checking 52 Integrability, concept 4—6 Integrability, consequences and practical applications 31 Integrability, multi-species processes 51 Integrability, scattering amplitude 101 Integrable systems, algebraic properties 50—51 Integrable systems, nearest neighbour processes 47 Integrable systems, quantum spin models 51 Integrable systems, relaxation times 63 Integrable systems, stochastic processes 6 30—52 Integral counterterms 298 299 341 Integral representation, energy expression 86 Integration measure, analytical continuation 309—310 Integration measure, normalization 286 378 379 451—452 Interacting particle systems, free fermion nature 199—200 Interacting particle systems, quantum Hamiltonian formalism 41—50 Interacting particle systems, stochastic dynamics 3—4 interactions see also Long-range interactions Short-range Interactions on site 6 Interactions, attractive 199 441—442 Interactions, contraction 383—384 Interactions, exclusion 86 114—115 116 Interactions, local 68—69 Interactions, repulsive 84 368 435 Interactions, time-ordered disorder 392 Interface, dynamics 76 231 Interface, fluctuations 79 Interface, growth 104 158 Interparticle distribution function 184 Ionic conductors, modelling 159 IR see Infrared Ising energy 36 Ising energy, spin configuration 32 Ising fixed point 432 433 Ising model 32—35 47 Ising model, bond disorder 433 Ising model, energy function 48 Ising model, geometrical description 430—431 Ising model, high-temperature expansion 257 408 431 Ising model, Kawasaki dynamics 68 Ising model, kinetic 76 185 186 187 Ising model, low-temperature expansion 256 408 431 Ising model, one-dimensional 13 154 156 162 191 Ising model, partition function 431 Ising model, planar 230 Ising model, random bond 260 430 433 Ising model, singularities 430 431 Ising model, spin configuration 33 Ising model, two-phase 231 Ito (prepoint) discretization 377 387 392 Jordan — Wigner transformation 175 177—178 Kardar — Parisi — Zhang (KPZ) equation 52 158 Kawasaki spin-flip dynamics 43 68 108 Ladder operators 20 35—36 107 Lame coefficients 268 Landau — Ginzburg — Wilson theory 440 442 445 446 Langevin approach 4 234 235 236 377—380 385 390—391 394 Laplace, equation 412 422 452 Laplace, transform 315 Large canonical ensemble 80 Late time behaviour see Asymptotic behaviour Lattice, Brownian motion 9 Lattice, Burgers equation 104 Lattice, derivative, density profile 130—131 Lattice, diffusion, with absorbing boundary 170 Lattice, equation, solution 173 Lattice, gas, as model system 8—9 13 Lattice, gas, collective velocity 147 Lattice, gas, diffusive 157—158 Lattice, gas, driven 3 103—161 171 Lattice, gas, hardcore 41—45 Lattice, gas, multi-species 16 97 Lattice, gas, one-dimensional 8—10 Lattice, gas, particle number conservation 55 Lattice, gas, shock 124—125 Lattice, gauge theory 256 408 Lattice, random walk 23 82 412 Lattice, sawtooth configuration 231 232 235 Lattice, sites, finite number of particles 6 Lattice, spacing, vanishing 62 Laurent expansion 299 342 343—344 Length scales, separate 131 149 171 Lenz, W. 32 Lie algebra 34 158 Light, cone 141—142 Light, scattering methods 385 Lipid bilayers 261 262 see Local current, time evolution 158 Local divergences 282—284 380—381 395—396 Local field theory 317 Localization lengths 145 149 173 174 Long-range interactions and fractal phase 277 Long-range interactions and phase transitions 125 Long-range interactions in membranes 272 Long-range interactions, competition 363 Long-range interactions, correlated disorder 404 407—408 Long-range interactions, hydrodynamic 387 Long-range interactions, nonrenormalization 303—305 Long-range interactions, one-dimensional systems 54 Long-range interactions, physical importance 305 Long-range interactions, tethered membranes 304—305 Longitudinal projectors, Fourier representation 454—456 Low-density phase 134 135 139 140 142 145 146 171 Low-dimensional systems 4 Low-temperature expansion, Ising model 256 408 431 Macroscopic mechanisms 6 7 magnetic susceptibility 32 magnetization 5 230 233 Magnons 36—37 Manifold, closed compact 421 Manifold, compact 422 Manifold, free Gaussian 435 Manifold, generalized model 430 Manifold, integrals 459—460 Manifold, isotropic 404 Manifold, single noninteracting 428 Manifold, size 427 Manifold, theory 408—409 Many body systems, conservation laws 32 Many body systems, exact solutions 30—31 33 34 Many body systems, master equation 5 Many body systems, modelling 3—4 23—27 Many body systems, tensor basis 23—26 Markov process, generator 18 Markov property 5 17 Massive see Bulk Master equation and conditional probability 84—85 Master equation, ASEP 114 Master equation, biased single-particle diffusion 63 Master equation, boundary terms 91 Master equation, determinant representation 158 Master equation, formulation 4 102 Master equation, Markov property 5 Master equation, quantum Hamiltonian formulation 17—29 Master equation, stationary form 59 Master equation, symmetric simple exclusion process (SSEP) 10 Master equation, three-particle 117 Master equation, two-particle 85 117 Master equation, vector form 21 Matrix algebra 96 101 159 160 Matrix product ansatz 52 90 137 159 161 Matrix representation 50 53 97 Matrix, time-dependent 91 Maximal current 133—134 143 144 146 155 157 Maximal transport capacity 135 147 Mean field analysis and variational approximation 354 Mean field analysis, continuum limit 172 Mean field analysis, diffusion-limited pair annihilation 195—197 Mean field analysis, domain wall dynamics 135 Mean field analysis, limitations 4 Mean field analysis, membranes 265—267 Mean field analysis, pertubative expansion 348—349 Mean field analysis, phase diagram 126 127 Mean field analysis, tubular phase 375 Membranes see also Fluid membranes Membranes of arbitrary dimension 258 Membranes with intrinsic disorder 278—279 Membranes, 6-expansion 256 349 Membranes, characteristic function 361 Membranes, density 422 423 425 427 Membranes, fluctuations 267 Membranes, Hamiltonian 278 Membranes, local field theory 317 Membranes, mean field description 265—267 Membranes, N-coloured 408—434 Membranes, O(N) model generalization 421—426 Membranes, partition function 359—361 Membranes, properties 261—279 Membranes, self-avoiding 319 Membranes, self-energy 361 Membranes, tethered (polymerized) 262—265 Membranes, tricritical point 363 Membranes, tubular phase 374—377 Membranes, two-loop calculations 350 Mermin — Wagner theorem 272 Messenger RNA see Biopolymerization Minimal current phase 144 152 153 Minimal sensitivity 350 354—355 Minimal subtraction (MS) 299 340—342 Model A 259 377 Modelling 3—4 6—13 43 47 104 215—223 258—261 Molecular dynamics algorithm 377 Molybdenum disulphide, folded phase 274 Momentum space formulation 95 459 Monte Carlo methods in modelling 5 Monte Carlo methods, equilibrium systems 57 Monte Carlo methods, gel electrophoresis 216 Monte Carlo methods, phase transitions 151 152 153 154 Monte Carlo methods, taking averages 28 Monte Carlo methods, TASEP 144 Monte Carlo methods, traffic models 157 Monte Carlo methods, two-loop diagrams 347 MOPE see Multilocal operator product expansion (MOPE) Multi-time correlation functions 74 Multilocal operator product expansion (MOPE) in renormalization 419 Multilocal operator product expansion (MOPE) in Taylor expansion 321—322 Multilocal operator product expansion (MOPE), coefficients in renormalization 298—299 Multilocal operator product expansion (MOPE), coefficients, evaluation 292—297 372 461—463 464 Multilocal operator product expansion (MOPE), coefficients, factorization 334 345—346 372—373 Multilocal operator product expansion (MOPE), coefficients, integral 341 Multilocal operator product expansion (MOPE), coefficients, Laurent series 343—344 Multilocal operator product expansion (MOPE), coefficients, residue extraction 310—313 Multilocal operator product expansion (MOPE), definition 291—292 Multilocal operator product expansion (MOPE), dipole contraction 360 Multilocal operator product expansion (MOPE), dipole divergence 418 Multilocal operator product expansion (MOPE), disordered system 395—396 Multilocal operator product expansion (MOPE), dynamic case 381—385
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