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Cardy J. — Scaling and renormalization in statistical physics
Cardy J. — Scaling and renormalization in statistical physics

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Название: Scaling and renormalization in statistical physics

Автор: Cardy J.


This text provides a thoroughly modern graduate-level introduction to the theory of critical behavior. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behavior, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behavior, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding the need for Feynman diagrams.

Язык: en

Рубрика: Физика/Термодинамика, статистическая физика/Квантовые методы/

Статус предметного указателя: Готов указатель без номеров страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 238

Добавлена в каталог: 22.08.2005

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Предметный указатель
$\epsilon$-expansion accuracy
$\epsilon$-expansion cubic symmetry breaking
$\epsilon$-expansion irrelevant operators
$\epsilon$-expansion Ising model
$\epsilon$-expansion O(n) model
$\epsilon$-expansion surface critical behaviour
Amplitudes universal ratios      
Anisotropic scaling      
Anisotropy spatial      
Anisotropy uniaxial      
Annealed disorder      
Anomalous dimension      
asymptotic freedom      
Bicritical point      
Block spin transformation      
Blume — Capel model      
boundary conditions      
Boundary conditions fixed      
Boundary conditions free      
Boundary conditions periodic      
Brownian motion      
Cellular automaton      
Central charge      
Coarse graining      
Coexistence curve      
Coleman's theorem      
Complex coordinates      
Compressibility, isothermal      
Confluent singularities      
Conformal anomaly number      
Conformal mapping      
Conformal transformations      
continuum limit      
Corrections to scaling      
Correlation functions      
Correlation functions critical exponents      
Correlation functions density — density      
Correlation functions dynamic      
Correlation functions multipoint      
Correlation functions Ornstein — Zernicke form      
Correlation functions orthogonality of two-point functions      
Correlation functions spin — spin      
Correlation functions three-point functions      
Correlation functions transformation law      
correlation length      
Correlation length critical behaviour      
Correlation length strip geometry      
Correlation length transformation law      
Critical dynamics      
Critical dynamics continuum models      
Critical dynamics detailed balance      
Critical dynamics directed percolation      
Critical dynamics discrete models      
Critical dynamics dynamic exponent      
Critical dynamics dynamic scaling      
Critical dynamics effect of other diffusive modes      
Critical dynamics far from equilibrium      
Critical dynamics Glauber model      
Critical dynamics Kawasaki model      
Critical dynamics model A      
Critical dynamics model B      
Critical dynamics non-dissipative terms      
Critical dynamics renormalization group approach      
Critical dynamics response field      
Critical dynamics response functional      
Critical end point      
Critical exponents      
Critical exponents branched polymers      
Critical exponents continuously varying      
Critical exponents directed percolation      
Critical exponents dynamic      
Critical exponents ferromagnet      
Critical exponents from the renormalization group      
Critical exponents Gaussian fixed point      
Critical exponents hyperscaling relation      
Critical exponents mean field values      
Critical exponents percolation      
Critical exponents scaling relations      
Critical exponents self-avoiding walks      
Critical exponents simple fluid      
Critical exponents surface exponents      
Critical isotherm      
Critical surface      
Cross-over behaviour      
Cross-over behaviour cross-over exponent      
Cross-over behaviour cross-over temperature      
Cross-over behaviour due to quenched disorder      
Cross-over behaviour in a random field      
Cross-over behaviour long-range interactions      
Cross-over behaviour multiple cross-overs      
Cross-over behaviour percolation      
Cross-over behaviour quantum to classical      
Cross-over behaviour scaling function      
Crystalline fields      
Cubic symmetry breaking      
Curie temperature      
Detailed balance, principle of      
Dimensional reduction      
Dimensional reduction branched polymers      
Dimensional reduction random field Ising model      
Dimensional transmutation      
Directed percolation      
Directed percolation critical exponents      
Directed percolation upper critical dimension      
Discontinuity fixed points      
Duality Ising model      
Duality XY model      
Dynamic critical behaviour      
Einstein relation      
Energy density      
Energy density near a boundary      
Extrapolation length      
Ferromagnet critical exponents      
Ferromagnet dilute      
Ferromagnet dynamic coupling to phonons      
Ferromagnet Heisenberg      
Ferromagnet Heisenberg critical dynamics      
Ferromagnet Ising      
Ferromagnet n-component      
Ferromagnet uniaxial      
Ferromagnet uniaxial dipolar      
Ferromagnet XY or planar      
Feynman path integral      
Finite-size scaling      
Finite-size scaling amplitude — exponent relation      
Finite-size scaling free energy      
Finite-size scaling strip geometry      
Finite-size scaling susceptibility      
Fluctuation — dissipation relation      
Fluctuations corrections to mean field theory      
Fluctuations effects of      
Fluctuations in the random field Ising model      
Fluctuations longitudinal and transverse      
Fluctuations near a boundary      
Fluctuations thermal v. quantum      
Fluids binary      
Fluids simple      
Fluids simple critical exponents      
Fluids simple models      
Free energy      
Free energy finite-size scaling      
Free energy in strip geometry      
Free energy quenched average      
Free energy reduced      
Free energy scaling form      
Free energy singular part      
Free energy transformation law      
Gaussian integration      
Gaussian model      
Gaussian model critical dynamics      
Gaussian model in random field      
Gaussian model in two dimensions      
Gaussian model surface critical behaviour      
Gaussian model Wick's theorem      
Gibbs distribution      
Ginzburg criterion      
Goldstone modes      
Griffiths singularities      
Harris criterion      
Heisenberg model      
High-temperature expansions      
Hyperscaling universal amplitude combination      
Hyperscaling violation above upper critical dimension      
Hyperscaling violation in random fields      
Imry — Ma criterion      
Irrelevant variables      
Irrelevant variables dangerous      
Ising model      
Ising model continuous spin version      
Ising model critical dynamics      
Ising model dilute      
Ising model dilute renormalization group approach      
Ising model duality      
Ising model existence of phase transition      
Ising model in a random field      
Ising model in a random field dimensional reduction      
Ising model in a random field Gaussian theory      
Ising model in a random field line shape      
Ising model in a random field lower critical dimension      
Ising model in a random field renormalization group approach      
Ising model in a random field upper critical dimension      
Ising model in a transverse field      
Ising model in one dimension      
Ising model lower critical dimension      
Ising model multicritical behaviour      
Ising model stress tensor      
Ising model surface critical behaviour      
Ising model upper critical dimension      
Ising model with vacancies      
Isotherms, liquid — gas      
Josephson scaling      
Kac formula      
Kepler's law      
Kosterlitz — Thouless criterion      
Landau theory      
Landau — Ginzburg model      
Landau — Ginzburg model time-dependent      
Laplace's equation      
Lattice animals      
Lattice gas      
Lifshitz point      
Limit cycles      
Long-range interactions      
Lower critical dimension      
Lower critical dimension continuous symmetries      
Lower critical dimension discrete symmetries      
Lower critical dimension random field Ising model      
Majority rule      
Marginal variables      
Marginal variables logarithmic corrections      
Master equation      
Mean field theory      
Mean field theory continuous symmetries      
Mean field theory correlation function      
Mean field theory critical exponents      
Mean field theory fluctuation corrections      
Mean field theory for surface critical behaviour      
Mean field theory free energy      
Mean field theory mean field equation      
Mermin — Wagner — Hohenberg theorem      
Models, relevance of      
Molecular field      
Monte Carlo dynamics      
Multicritical points      
Neel temperature      
Normal ordering      
O(n) model      
O(n) model $n\to 0$ limit
O(n) model 2 + $\epsilon$ expansion
O(n) model large n limit      
O(n) model lower critical dimension      
O(n) model mean field theory      
O(n) model near four dimensions      
O(n) model near two dimensions      
Operator product expansion      
Operator product expansion coefficients      
Operator product expansion in the Gaussian model      
Operator product expansion in two dimensions      
Operator product expansion with stress tensor      
Order parameter      
Ornstein — Zernicke form      
Osmotic pressure      
Partition function      
Peierls argument      
Percolation bond      
Percolation cluster size distribution      
Percolation critical exponents      
Percolation directed      
Percolation effects of finite temperature      
Percolation infinite cluster      
Percolation mapping to the Potts model      
Percolation mean cluster size      
Percolation upper critical dimension      
Phase transitions      
Phase transitions continuous      
Phase transitions first-order      
Phase transitions first-order fluctuation-driven      
Polymers branched      
Polymers branched fixed topology      
Polymers branched upper critical dimension      
Polymers linear      
Polymers linear at surfaces      
Polymers linear critical exponents      
Polymers linear Edwards model      
Polymers linear finite concentration      
Polymers linear Flory formula      
Polymers linear mapping to O(n) model      
Polymers linear radius of gyration      
Polymers linear random walk model      
Polymers linear self-avoiding walk model      
Polymers linear theta point      
Polymers linear upper critical dimension      
Population dynamics      
Potts model      
Potts model continuous spin version      
Potts model critical behaviour      
Potts model upper critical dimension      
Quantum effects      
Quantum electrodynamics      
Quasi-long range order      
Quenched disorder      
Quenched disorder random fields      
Quenched disorder self-averaging quantities      
Random fields      
Random fields cross-over behaviour      
Random fields hyperscaling violation      
Reduced hamiltonian      
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