Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Collective Behavior, from particles to fields : Introduction, Phonons &
elasticity, Phase transitions, Critical Behavior.
- Statistical Fields : Introduction, The Landau-Ginzburg Hamiltonian,
Saddle point approximation and mean field theory, Continuous symmetry breaking
and Goldstone modes, Discrete symmetry breaking and domain walls.
- Fluctuations : Scattering and fluctuations, Correlation functions and
susceptibilities, Lower critical dimension, Comparison to experiments, Gaussian
integrals, Fluctuation corrections to the saddle point, The Ginzburg criterion.
- The scaling hypothesis : The homogeneity assumption, Divergence of
correlation length, Critical correlation functions and self similarity, The
renormalization group (conceptual), The renormalization group (formal), The
Guassian model (direct solution), The Gaussian model (renormalization group).
- Perturbative renormalization group : Expectation values in the Gaussian
model, Expectation values in perturbation theory, Diagrammatic representation
of perturbation theory, Susceptibility, Perturbative RG (first order),
Perturbative RG (second order), The epsilon expansion, Irrelevance of other
interactions, Comments on the epsilon expansion.
- Lattice systems : Models and methods, Transfer matrices, Position space
RG in one dimension, The Niemeijervan-Leeuwen cumulant approximation, The
Migdal-Kadanoff bond moving approximation, Monte Carlo simulations.
- Series expansions : Low temperature expansions, High temperature
expansions, Exact solution of the one dimensional Ising model, Self duality in
the two-dimensional Ising model, Dual of the three dimensional Ising model,
Summing over phantom loops, Exact free energy of the square lattice Ising
model, Critical behavior of the two-dimensional Ising model.
- Beyond spin waves : The nonlinear sigma model, Topological defects in the
XY model, Renormalization group for the Coulomb gas, Two-dimensional solids,
Two-dimensional melting.
- Dissipative dynamics : Brownian motion of a particle, Equilibrium
dynamics of a field, Dynamics of a conserved field, Generic scale invariance in
equilibrium systems, Non-equilibrium dynamics of open systems, Dynamics of a
growing surface.
- Mehran Kardar, Statistical Physics of Fields.
- P. M. Chaikin & T. C. Lubensky, Principles of condensed matter physics.
