PH6008: Monte-Carlo Methods in Statistical Physics
Syllabus
Module 1: Introduction
Lecture hours: 8 · Tutorial hours: 0 · Lab hours: 0
Statistical Mechanics: basic concepts, Monte Carlo (MC) method for sampling and importance sampling, Detailed balance, Metropolis algorithm, acceptance criterion, Random numbers .
Module 2: Monte Carlo simulation of lattice and off-lattice systems
Lecture hours: 10 · Tutorial hours: 0 · Lab hours: 0
The Lennard-Jones system, boundary conditions, truncation of potential, neighbourlist, Trial moves, calculation of thermodynamic averages, The Ising model and its phase behavior, MC simulations in various ensembles: NVT, NPT, μVT .
Module 3: Free energy calculation and phase equilibria
Lecture hours: 6 · Tutorial hours: 0 · Lab hours: 0
Thermodynamic integration, Widom insertion method for chemical potential, Gibbs ensemble, Gibbs-Duhem integration .
Module 4: Histogram Methods
Lecture hours: 8 · Tutorial hours: 0 · Lab hours: 0
Rare events, estimation of free energy barriers and rates, Umbrella sampling, histogram reweighting, Wang-Landau sampling .
Module 5: Optimization, biased and accelerated sampling
Lecture hours: 10 · Tutorial hours: 0 · Lab hours: 0
Simulated annealing, Replica exchange MC (parallel tempering), Configuration bias MC, restricted ensemble MC, swap MC, Cluster algorithms and critical behavior (finite size scaling), Hybrid MC .
Study Materials
Textbooks
- Understanding Molecular Simulation: From Algorithms to Applications, Daan Frenkel and Berend Smit, , ISBN: 0122673514
- Computer Simulation of Liquids, Michael P. Allen and Dominic J. Tildesley, 2nd Edition, ISBN: 0198803206
References
- A Guide to Monte Carlo Simulations in Statistical Physics, David P. Landau and Kurt Binder, 4th Edition, ISBN: 1107074029
- Monte Carlo Methods in Statistical Physics, M. E. J. Newman and G. T. Barkema, , ISBN: 0198517971