Monte-Carlo-Methods

This repository contains implementations of various Monte Carlo methods used in statistical mechanics and other fields. The methods and models covered in this repository include:

• Random Walk: Simulations and analysis of random walk processes.
• Percolation: Models and simulations of percolation theory.
• Ising Model: Implementation and analysis of the Ising model in statistical physics.
• Potts Model: Simulations of the Potts model.
• XY Model: Implementations of the XY model. (in progress)
• Sign Problem: Exploration and solutions for the sign problem in Monte Carlo simulations. (in progress)

Statistical Mechanics

These notebooks are designed to help you understand and solve problems related to Monte Carlo simulations in statistical mechanics, as inspired by the book "Monte Carlo Simulation in Statistical Physics" by Binder & Heermann.

Contents

• mcm_randomwalk.ipynb: Introduction and simulations of random walk processes.
• mcm_percolation.ipynb: Implementation of percolation theory.
• mcm_ising.ipynb: Simulation of the Ising model.
• mcm_Potts.ipynb: Simulation of the Potts model.
• mcm_nonuniformrandomnumbers.ipynb: Scripts for generating non-uniform random numbers.
• mcm_randomwalk-checkpoint.ipynb: Checkpoint notebook for random walk simulations.

Getting Started

To get started, clone the repository and open any of the Jupyter Notebooks to explore the simulations and analyses.

git clone <repository-url>
cd Monte-Carlo-Methods
jupyter notebook <notebook-name>.ipynb

Contributions

Contributions are welcome! Please feel free to submit issues or pull requests.

License

This project is licensed under the Apache-2.0 License - see the LICENSE file for details.

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This is my first repository. I hope you find it useful.