Spring 2020, Jacobus Verbaarschot
Phase Transitions, Order of a phase transition, Thermodynamic limit, Spin models
Landau-Peirels argument, Phases in 2d, Spontaneous symmetry breaking
Fluctuations dissipation theorem, Critical Exponents, Scaling
Two-parameter scaling, Landau Ginzburg theory
Critical exponents of Landay Ginxburg theory, Inhomogeneous systems, Two-point correlation function
Ginzburg Criterium, Central Limit Theorem, Universality --still to be scscanned
1d Ising model, Transfer matrix, Correlation function
Low T expansion, High T expansion, Mean Field Theory, Kramers-Wannier duality
Onsager Solution of 2d Ising Model
Solution of the 2d Ising Model, Tensor representation
Discussion of the solution of the 2d Ising model
XY Model
Heisenberg model
Heisenberg Model
Solution Heisenberg model
Goldstone's theorem
Coleman-Mermin-Wagner theorem, Kosterliz-Thouless transition
Physical picture of Kosterliz-Thouless transition
Monte-Carlo simulations, Markov chains, Detailed balance
Perron's theorem, Heat bath algorithm, Langevin equation, Fokker-Planck equation
Stability analysis, Microcanonical simulations, Critical slowing down.
Anomalouos dimensions, Kadanoff theory.
Correlation function, Renormalization group
Fixed Points, Classification, Renormalization group transformation
Renormalization group for triangular Ising Model, Nienhuis-Nauenberg criterion, Crossover transition, Finite size scaline, $\epsilon$-Expansion.
$\epsiolon$ expansion, Gaussian model, Wilson-Fisher fixed point, Dangerous irrelevant variables.
One loop renormalization of the \phi^4 model
Two loop renormalization of the \phi^4 model Analysis of renormalization group equations. Critical exponents of \phi^4 theory.
Entanglement entropy.
Examples of entanglement entropy. Volume law. Area law.
Srednicki's calculation.
Ryu-Takayangi formule. Tow-body SYK model.
Path integral formulation of the SYK model. Mean field theory. (Added handwritten notes)
Conformal invariance. Large q expansion. Entropy.
Spectral density of the SYK model.