EP 413 Advanced Statistical Mechanics ( 2018-2019 )
Instructor: Amitabh Nandi
Part 2: Critical phenomena - Phase transitions, critical exponents, Yang-Lee theorems, lattice gas model, 1D Ising model and transition matrix formalism, duality relation for the 2D square lattice Ising model, mean field theories, Landau Ginzburg statistical field theory, saddle point approximation, Gaussian model, scaling hypothesis, renormalisation group (RG), position space RG in 1D Ising model
Course Name: Advanced Statistical Mechanics (EP413)
Course Type: Theory ( Honours / Elective )
Credits: 6
Prerequisites: No formal prerequisites, but a basic knowledge of statistical mechanics is assumed.
Course Content:
Part 1: Stochastic processes - Markov processes, Chapman-Kolmogorov equations, master equation, solution techniques for various master equations, W-matrix formalism, Langevin equation, Fokker-Planck equation, Ito and Stratonovich conventions of stochastic calculus, diffusion and first-passage problems.
Part 2: Critical phenomena - Phase transitions, critical exponents, Yang-Lee theorems, lattice gas model, 1D Ising model and transition matrix formalism, duality relation for the 2D square lattice Ising model, mean field theories, Landau Ginzburg statistical field theory, saddle point approximation, Gaussian model, scaling hypothesis, renormalisation group (RG), position space RG in 1D Ising model
Also Kinetic Monte-Carlo method (Gillespie algorithm), Monte Carlo simulations
Books/Other Resources:
For part 1: Stochastic Processes in Physics and Chemistry (van Kampen), Elements of Nonequilibrium Statistical Mechanics (Balakrishnan)
For part 2: Statistical Physics (Huang), Statistical Physics of Fields (Kardar), Equilibrium statistical physics (Plischke and Bergersen), Exactly Solved Models in Statistical Mechanics (Baxter)
For part 2: Statistical Physics (Huang), Statistical Physics of Fields (Kardar), Equilibrium statistical physics (Plischke and Bergersen), Exactly Solved Models in Statistical Mechanics (Baxter)
Lecture notes on statistical field theory by David Tong (for part 2 of the course): http://www.damtp.cam.ac.uk/user/tong/sft.html
Attendance:
No attendance requirement
Tutorials/ Exams Grading:
Tutorial problems (ungraded) were of medium to difficult kind. The instructor discussed solutions to the harder problems before midsem/endsem.
3 quizzes (best 2out of 3 were considered), midsem, endsem, along with a project.
Pro tips:
Don't expect the instructor to work out all the steps in class. Some amount of self-study is definitely necessary to get through the course comfortably.
Respondent: Arkya Chatterjee
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