The Theory of Critical Phenomena : an Introduction to the Renormalization Group.

The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Binney, J. J.
Otros Autores: Dowrick, N. J., Fisher, A. J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Oxford : Clarendon Press, 1992.
Temas:
Renormalization group.
Critical phenomena (Physics)
Mathematical physics.
Groupe de renormalisation.
Phénomène critique (Physique)
Physique mathématique.
SCIENCE > Energy.
SCIENCE > Mechanics > General.
SCIENCE > Physics > General.
Mathematical physics
Renormalization group
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Contents
  • 1 Introduction
  • 1.1 Continuous phase transitions and critical points
  • 1.1.1 Divergences and critical exponents
  • 1.1.2 Fluctuations and critical opalescence
  • 1.2 The order parameter
  • 1.2.1 Liquid-gas transition
  • 1.2.2 Binary fluids
  • 1.2.3 Ferromagnetic/paramagnetic transition
  • 1.2.4 Anti-ferromagnetic/paramagnetic transition
  • 1.2.5 Helium I/helium II transition
  • 1.2.6 Conductor/superconductor transitions
  • 1.2.7 Helium three
  • 1.3 Correlation functions
  • 1.4 Universality
  • 1.5 Thermodynamic potentials.
  • 1.5.1 The Widom and Kadanoff scaling hypotheses
  • 1.6 Why study phase transitions?
  • Problems
  • 2 Statistical mechanics
  • 2.1 Thermodynamic quantities
  • 2.2 Fluctuations and correlation functions
  • 2.3 Metastability and spontaneous symmetry breaking
  • 2.3.1 Metastability
  • 2.3.2 Spontaneous symmetry breaking
  • Problems
  • 3 Models
  • 3.1 Description of models
  • 3.1.1 The Ising model
  • 3.1.2 The lattice gas
  • 3.1.3 ß-brass
  • 3.1.4 The XY and Heisenberg models
  • 3.1.5 Potts model
  • 3.1.6 Gaussian and spherical models
  • 3.1.7 Percolation model.
  • 3.2 Transfer matrices and the Ising ring
  • 3.2.1 Solution of the Ising ring
  • 3.2.2 Correlation functions
  • 3.3 The partition function of the spherical model
  • 3.4 High-temperature expansions and the Ising model
  • 3.4.1 High-temperature expansions
  • 3.4.2 The partition function of the Ising model
  • 3.4.3 The correlation functions of the Ising model
  • 3.4.4 Numerical evaluation of high-temperature expansions
  • Problems
  • 4 Numerical simulations
  • 4.1 Direct evaluation of thermal averages
  • 4.2 Sampling configurations
  • 4.2.1 Importance sampling.
  • 4.2.2 General structure of numerical algorithms
  • 4.3 Monte Carlo methods
  • 4.3.1 The Metropolis algorithm
  • 4.4 Molecular dynamics
  • 4.4.1 Ergodicity and integrability
  • 4.4.2 From microcanonical to canonical averages
  • 4.5 Langevin equations
  • 4.5.1 Comparison of the Langevin and molecular-dynamics methods
  • 4.6 Independence of configurations
  • 4.6.1 Correlations along the path
  • 4.6.2 Critical slowing down
  • 4.6.3 The Swendsen-Wang algorithm
  • 4.6.4 The Wolff algorithm
  • 4.7 Calculation of critical exponents from simulations
  • Problems
  • 5 Real-space renormalization.
  • 5.1 Renormalizing the lattice
  • 5.2 Block variables
  • 5.3 The renormalization of the Hamiltonian
  • 5.3.1 Fixed points
  • 5.3.2 The calculation of v
  • 5.4 The renormalization of B, M, X and G[sub(c)]
  • 5.4.1 The value of }
  • 5.4.2 Non-zero external field
  • 5.4.3 The renormalization of M, { and G[sub(c)]
  • 5.4.4 Critical exponents for the renormalized model
  • 5.5 The critical exponents for T = T[sub(c)]
  • 5.5.1 The exponent j
  • 5.5.2 The exponent e
  • 5.6 The critical exponents for T T[sub(c)]
  • 5.6.1 The exponent Ý
  • 5.6.2 The exponent Þ
  • 5.6.3 The exponent Ü

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