Ising Model Simulation

You can try it online!

Features

• Visualize the spin configuration.
• Display the quantities: Energy $\frac{E}{N}$, magnetization $\frac{M}{N}$, heat capacity $\frac{C}{k_{\mathrm{B}} N}$, and susceptibility $\frac{\chi}{N}$.
• You can adjust the parameters: Temperature $k_{\mathrm{B}} T$, size $N$, allowed states $\sigma$, coupling constants $J$, and external field $h$.
• You can select the algorithms: The Metropolis algorithm and the heat bath algorithm.

• Plot the temperature dependence of the quantities.

To plot the graphs:

1. Set the temperature to start cooling from.
2. Click Cool the system and plot graphs.

Examples

External Field

1. Press Reset to default.
2. Adjust external field $h$.

Antiferromagnetism

1. Press Reset to default.
2. Set horizontal and vertical coupling constants $J$ to −1.

Frustration on a Triangular Lattice

1. Press Reset to default.
2. Set horizontal, vertical, and one of diagonal coupling constants $J$ to −1.

One-Dimensional

1. Press Reset to default.
2. Set size $N$ to 20 × 1.
3. Set vertical coupling constant $J$ to 0.

Collinear State

1. Press Reset to default.
2. Set horizontal, vertical coupling constants $J$ to 0.
3. Set two diagonal coupling constants $J$ to −1.

Spin-1 Boson

1. Press Reset to default.
2. Add a new allowed state 0. Now we have $\sigma = 1, 0, -1$.

Development

I learned the Ising model on a statistical mechanics lecture at university and was interested in it. I started working on this project on November 2025.

I wrote this project in HTML, CSS, and JavaScript.

• This project formats the codes thanks to Prettier.
• This project lints the codes thanks to ESLint.
• The website displays mathematics thanks to KaTeX.

Except for KaTeX, this project has no runtime dependencies.

This is a hobby project of mine I started from scratch. I did not use generative AI for this project.