Ising Model Simulation using Metropolis-Hastings Algorithm

Overview

This repository contains a Python implementation of the Ising model simulation using the Metropolis-Hastings algorithm. The code allows for studying phase transitions in magnetic systems, computing specific heat, mean energy, magnetization, and magnetic susceptibility for a given lattice.

Features

• Generate random 2D Ising spin configurations
• Compute system energy with free and periodic boundary conditions
• Simulate spin dynamics using the Metropolis-Hastings algorithm
• Compute specific heat, mean energy, magnetization, and magnetic susceptibility
• Support for periodic boundary conditions (PBC)
• Support for triangular and square lattices
• Visualise frustrated magnetism

Installation

Clone the repository and install the required dependencies:

git clone https://github.com/SuvamT0071/Metropolis-Hastings-in-CMP.git
cd Metropolis-Hastings-in-CMP/isingmetro
pip install -r requirements.txt

Alternatively, install dependencies manually:

pip install numpy matplotlib tqdm

To install isingmetro, use pip:

pip install isingmetro

or

pip install git+https://github.com/SuvamT0071/Metropolis-Hastings-in-CMP.git

Usage

1. Generate a Random Grid

from isingmetro import grid_maker

grid = grid_maker(nrows=10, ncols=10)
print(grid)

2. Compute Energy

from isingmetro import compute_energy

energy = compute_energy(grid)
print("Energy:", energy)

3. Run the Ising Model Simulation

from isingmetro import ising_model

nsamples = 10000
temperature = 2.5
saved_energies, final_grid = ising_model(nsamples, temperature, grid)
print("Final Grid:", final_grid)

4. Compute Specific Heat

from isingmetro import specific_heat

temp_range = [1.0, 2.0, 3.0, 4.0]
Cv, updated_Cv = specific_heat(grid, temp_range)
print("Specific Heat:", Cv)

5. Compute Magnetization

from isingmetro import magnetize

magnetization = magnetize(grid, temp_range)
print("Magnetization:", magnetization)

Periodic Boundary Conditions (PBC) Implementation

The repository also provides functions to compute system properties using periodic boundary conditions. Example:

from isingmetro import compute_energy_PBC

energy_pbc = compute_energy_PBC(grid)
print("Energy with PBC:", energy_pbc)

Contributing

If you'd like to contribute to improving this repository, feel free to submit a pull request.

Credit

This code was written by Suvam Tripathy, a Masters' of Physics student(2023-2025) of Indian Institute of Technology, Madras, as a part of a mini-project.

License

This project is licensed under the MIT license.