Illustrating various topics in classical and quantum statistical mechanics through Monte Carlo simulations .
Physical and mathematical subjects that are addressed include:
- Introduction to direct and Markov-chain Monte Carlo sampling
- Equivalence of Newton and Boltzmann mechanics, classical Monte Carlo simulations
- Entropic interactions and a liquid-gas phase transition
- Monte Carlo integration
- Quantum statistical mechanics: path integral representation of the density matrix, quantum Monte Carlo simulations
- Bose-Einstein condensation
- The Ising model of ferromagnetism
The material presented here closely follows "Statistical Mechanics: Algorithms and Computations" by W. Krauth from the École normale supérieure and "Statistical Mechanics: A Set of Lectures" by R. P. Feynman.
- Some resources are obtained from https://github.com/dgoekmen/Statistical-Mechanics with LISENCE retained.