Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- Part one Statics -- 1 Spin systems and fluids -- 1.1 Spin models -- 1.1.1 Ising hamiltonian -- 1.1.2 Vector spin models -- 1.1.3 Thermodynamics of Ising models -- Positivity of C -- 1.1.4 Spin density and energy density variables -- 1.1.5 Hydrodynamic fluctuations of temperature and magnetic field -- 1.2 One-component fluids -- 1.2.1 Canonical ensemble -- 1.2.2 Grand canonical ensemble -- Field variables and density variables -- Shift of the origin of the one-particle energy -- Lattice gas model -- 1.2.3 Thermodynamic derivatives and fluctuation variances -- 1.2.4 Gaussian distribution in the long-wavelength limit -- Weakly inhomogeneous cases -- Thermodynamic stability -- 1.2.5 Fluctuating space-dependent variables -- 1.2.6 Density correlation -- 1.2.7 Hydrodynamic temperature and pressure fluctuations -- 1.2.8 Projection onto gross variables in the hydrodynamic regime -- 1.2.9 Pressure, energy, and elastic moduli in terms of g(r) -- Generalization to the binary fluid mixture case -- 1.3 Binary fluid mixtures -- 1.3.1 Grand canonical ensemble -- 1.3.2 Fluctuating density variables -- 1.3.3 Molar and mass concentrations -- 1.3.4 Hydrodynamic fluctuations of the field variables -- Projection of Pi onto the hydrodynamic variables -- 1.3.5 The direct correlation functions and the hydrodynamic hamiltonian -- Appendix 1A Correlations with the stress tensor -- References -- 2 Critical phenomena and scaling -- 2.1 General aspects -- 2.1.1 Critical exponents and correlation functions -- Order parameter correlation -- Energy correlation -- 2.1.2 Fractal dimensions -- Finite systems at the critical point -- Fisher cluster model -- 2.1.3 Scaling ansatz -- 2.1.4 Two-scale-factor universality -- 2.1.5 Parametric representation of equations of state -- Ising systems -- One-component fluids.

2.2 Critical phenomena in one-component fluids -- 2.2.1 Mapping relations -- Critical isochore -- Coexistence-curve diameter -- The Clausius-Clapeyron relation -- 2.2.2 Thermodynamic derivatives and the two-scale-factor universality -- 2.2.3 Temperature and pressure fluctuations -- Adiabatic T-p relation on the coexistence curve -- 2.2.4 Gravity effects in one-component fluids -- 2.3 Critical phenomena in binary fluid mixtures -- 2.3.1 Mapping relations -- Leung and Griffiths' theory -- 2.3.2 Concentration fluctuations -- 2.3.3 Temperature and pressure fluctuations -- 2.3.4 Azeotropy and the dilute limit -- 3He-4He mixtures near the gas-liquid critical line -- Dilute mixtures -- 2.3.5 Incompressible limit -- 2.3.6 Two-scale-factor universality in the isobaric case -- 2.4 4He near the superfluid transition -- 2.4.1 Singular and nonsingular density variables -- 2.4.2 Thermodynamic derivatives -- 2.4.3 Temperature and pressure fluctuations -- 2.4.4 Gravity effects in 4He -- Height-dependent reduced temperature -- Gravity-induced two-phase coexistence -- Appendix 2A Calculation in non-azeotropic cases -- References -- 3 Mean field theories -- 3.1 Landau theory -- 3.1.1 Order parameter and constrained free energy -- 3.1.2 Regular expansion of the Landau free energy -- 3.1.3 Thermodynamic derivatives in the Landau theory -- 3.1.4 Landau free energy including the energy variable -- 3.2 Tricritical behavior -- 3.2.1 Symmetrical tricriticality -- Nonvanishing ordering field -- 3.2.2 Scaling theory around a symmetrical tricritical point -- 3.2.3 Unsymmetrical tricriticality -- 3.3 Bragg-Williams approximation -- 3.3.1 Ising systems -- 3.3.2 Order-disorder phase transitions in bcc alloys -- 3.3.3 Order-disorder phase transitions in fcc alloys -- 3.4 van der Waals theory -- 3.4.1 Thermodynamics of one-component fluids -- Landau free energy -- Critical behavior.

Gradient free energy -- 3.4.2 Extension to binary fluid mixtures -- 3.5 Mean field theories for polymers and gels -- 3.5.1 Polymer solutions -- Solvent quality and semidilute solutions -- Chemical potentials -- Osmotic pressure and bulk modulus -- Coexistence and spinodal curves -- 3.5.2 Polymer blends -- Symmetric case -- 3.5.3 Polymer gels -- Isotropically swollen gels -- Gels under a constant uniaxial stretching force -- One-dimensionally constrained gels -- Remarks -- 3.5.4 Coil-globule transition in a single chain -- Appendix 3A Finite-strain theory -- References -- 4 Advanced theories in statics -- 4.1 Ginzburg-Landau-Wilson free energy -- 4.1.1 Gradient free energy -- 4.1.2 Gaussian approximation -- 4.1.3 Perturbation expansion and the critical dimension -- The Ginzburg number -- Exact relations -- 4.1.4 Feynman diagram expansion -- 4.1.5 Inclusion of the energy density -- 4.1.6 Hydrodynamic hamiltonian for n = 1 -- 4.2 Mapping onto fluids -- 4.2.1 One-component fluids -- 4.2.2 Binary fluid mixtures -- 4.2.3 4He near the superfluid transition -- 4.2.4 3He-4He mixtures near the Lambda line and the tricritical point -- 4.2.5 Polymer solutions -- 4.2.6 Polymer blends -- 4.2.7 Gravity effects -- Gravity-induced interface -- 4.2.8 Electric field effects in non-ionic fluids -- Shift of the critical temperature -- Effects on the critical fluctuations -- Critical electrostriction -- 4.3 Static renormalization group theory -- 4.3.1 Renormalization group equations for r and g (n = 1) -- Solution for… -- Mean field critical behavior -- Asymptotic critical behavior -- 4.3.2 Renormalization group equation for v (n = 1) -- Solution at criticality -- Crossover at small, positive Tau -- 4.3.3 Perturbation theory at g = g* and v = v* -- Exponentiation of logarithmic terms (n = 1) -- Higher-order perturbation calculations in n-component systems.

4.3.4 Singular free energy for general h and Tau in n-component systems -- Equation of state -- Specific heat -- 4.3.5 Results for Ising-like systems -- 4.3.6 Specific heats in classical fluids -- 4.3.7 Broken symmetry for… -- Transverse correlation length and the superfluid density -- 4.3.8 Hydrodynamic hamiltonian for… -- 4.4 Two-phase coexistence and surface tension -- 4.4.1 Interface profile and surface tension near the critical point -- Instability of the interface solution in many-component systems -- 4.4.2 Surface tension for the general free-energy density -- 4.4.3 Interface in symmetrical tricritical systems -- 4.4.4 Interface in polymer systems -- Semidilute polymer solutions -- Symmetric polymer blends -- Asymmetric polymer blends -- 4.4.5 Thermal interface fluctuations -- 4.4.6 Quantum interface fluctuations -- 4.5 Vortices in systems with a complex order parameter -- 4.5.1 Fundamental vortex solutions -- 4.5.2 Interaction between vortices -- 4.5.3 Fluid velocity at a vortex point -- Arms-Hama approximation -- Appendix 4A Calculation of the critical exponent Eta -- Appendix 4B Random phase approximation for polymers -- Appendix 4C Renormalization group equations for n-component systems -- 4He near the superfluid transition -- Appendix 4D Calculation of a free-energy correction -- Appendix 4E Calculation of the structure factors -- Appendix 4F Specific heat in two-phase coexistence -- References -- Part two Dynamic models and dynamics in fluids and polymers -- 5 Dynamic models -- 5.1 Langevin equation for a single particle -- 5.1.1 Brownian motion -- 5.1.2 Fokker-Planck equation for the velocity -- 5.1.3 Langevin equation for the position -- Diffusion constant in general -- 5.1.4 Compound-poissonian noise -- 5.1.5 Long-time tail -- 5.2 Nonlinear Langevin equations with many variables -- 5.2.1 General theory.

Time reversal and anti-symmetric kinetic coefficients -- 5.2.2 Probability distribution and Fokker-Planck equation -- 5.2.3 Time-correlation functions -- 5.2.4 Approach to equilibrium -- 5.3 Simple time-dependent Ginzburg-Landau models -- 5.3.1 Nonconserved systems: model A -- 5.3.2 Conserved systems: model B -- 5.3.3 Coupled systems: model C -- Steady states under a temperature (chemical potential) gradient -- 5.3.4 Mean field theory and thermodynamic stability -- Models A and B -- Model C -- 5.3.5 Critical dynamics in model A -- Dynamic renormalization group theory -- Yahata and Suzuki's calculation -- 5.3.6 Critical dynamics in model C -- 5.4 Linear response -- 5.4.1 Transport coefficients in fluids -- Viscosities -- Thermal conductivity -- Dissipative coupling in diffusion and heat conduction -- 5.4.2 General linear response to thermal disturbances -- Response to sound wave -- 5.4.3 Long-range correlations in steady states -- Appendix 5A Derivation of the Fokker-Planck equation -- Appendix 5B Projection operator method -- Linear projection -- Nonlinear projection -- Appendix 5C Time reversal symmetry in equilibrium time-correlation functions -- Appendix 5D Renormalization group calculation in purely dissipative dynamics -- Appendix 5E Microscopic expressions for the stress tensor and energy current -- References -- 6 Dynamics in fluids -- 6.1 Hydrodynamic interaction in near-critical fluids -- 6.1.1 Intuitive picture of random convection -- 6.1.2 Model H -- 6.1.3 Mode coupling theory -- Relaxation of the order parameter -- Frequency-dependent shear viscosity -- 6.1.4 Dynamic renormalization group theory -- 6.1.5 The Stokes-Kawasaki approximation -- 6.1.6 Transient electric birefringence (Kerr effect) -- 6.2 Critical dynamics in one-component fluids -- 6.2.1 Dynamic equations of compressible fluids -- Gravity effects -- Slow dynamics.

6.2.2 Cluster convection and enhanced heat conduction.