simulation

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:book: Algorithms in simulation: Markov chain Monte Carlo, Hybrid Monte Carlo, Heat Bath Algorithm, Path integral, Density matrices etc.

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# 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.

![Path integral Monte Carlo simulations](https://raw.githubusercontent.com/npshub/simulation/master/fig/snapshot_00043.png)

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

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