Simulation in Physics

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.

<img src="fig/ising.gif" width="200" height="200" /> <img src="fig/XY_small.gif" width="200" height="200" /> <img src="fig/heisenberg_small.gif" width="200" height="200" />

Reference:

1. Some resources are obtained from https://github.com/dgoekmen/Statistical-Mechanics with LISENCE retained.