Cardy J. — Scaling and renormalization in statistical physics
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Название: Scaling and renormalization in statistical physics
Автор: Cardy J.
Аннотация:
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.
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 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 limit O(n) model 2 + 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 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 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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