Global picture of evolution of macroscopic systems: nonlinear dynamics, 1-d and 2-d systems, fixed points, flowlines, population growth, Lotka-Volterra model etc [Strogatz "Nonlinear dynamics and chaos", ch.5, sec.6.1-6.4, sec.2.3].
Generalities on classical statistical physics, probabilistic approaches [K 4.1]; Microcanonical ensemble, 2-level systems, the ideal gas, mixing entropy [K 4.2-4.5]; Canonical ensemble, standard examples; Grand canonical ensemble.
Including interactions, perturbation theory; the virial expansion and van der Waals equation [K 5.1-5.3]; Condensation, mean field theory, liquid-gas transition [K 5.5].
Quantum statistical mechanics: examples -- dilute gases, vibrations in solids, phonons, specific heat [K 6.1-6.2]; very quick overview of blackbody radiation and the Planck resolution of the ultraviolet catastrophe [K 6.3]; quantum macrostates and the density matrix [K 6.5].
Ideal quantum gases and identical particles [K ch.7]: generalities [K 7.1]; grand canonical formulation [K 7.3]; nonrelativistic gases, high temperature limit [K 7.4]; degenerate Fermi gas [K 7.5]; degenerate Bose gas and Bose-Einstein condenation [K 7.6].
Discussion on some assignment questions: black hole thermodynamics, van der Waals fluid and condensation [from Goldenfeld, Pathria etc].
Electron lattice models, hopping etc; Lattices and spin systems; Ising model; 1-dim Ising model, the transfer matrix and the exact solution [H 14.6]; 1-dim quantum Ising model and exact solution via Jordan-Wigner and Bogolubov transformations etc [Sachdev "Quantum phase transitions", ch.5, 10.1]; 2-dim Ising model at finite temperature, Peierls droplets and phase transitions [H 14.3] [Polyakov "Gauge fields and strings", sec.1.3, pg.6-7].
Critical phenomena: general picture of phase transitions in magnetic systems; universality and critical exponents; correlation length and the spin-spin correlation function; Landau mean field theory and mean field critical exponents; some exponents for the tricritical point; relations between the various critical exponents, Fisher, Widom laws etc [H 16.1-4, 17.1, 17.4-6];
The scaling hypothesis and self-similarity near the critical point; Kadanoff block spins; 1-dim Ising model and block spin transformations via (i) the transfer matrix representation, (ii) explicit partial spin sums, and subsequent flows on coupling parameters [H 18.1-2] [P 14.2.A, 14.4.A]; 2-dim Ising model and block spin transformations by explicit partial sums on alternating spins, extra spin-spin interactions generated and Wilson's approximations leading to fixed points [P 14.2.C] [P 14.4.C]; general structure of RG flow transformations and fixed points.
From the scaling hypothesis for the free energy to critical exponents; Gaussian model action/free.energy and critical exponents, trivial fixed point [Altland-Simons, 8.3-8.4].
Momentum space renormalization; phi^4 theory and 1-loop Wilsonian renormalization via partial sum over fast modes; RG flow equations in [4-epsilon]-dimensions, the Wilson-Fisher fixed point and critical exponents [Altland-Simons, 8.4 esp 8.4.3-8.4.4] [Peskin ch.12.1]; general structure of RG flows, beta-functions, fixed points --> basic glimpse of conformal field theories.
* takehome midsem, assignment, endsem
Suggested follow-up reading: