This simulation is written in Rust and compiled to WebAssembly (WASM) for performance. It implements the 2D Ising model with periodic boundaries using multiple Monte Carlo algorithms. The website is written in plain HTML, CSS, and JavaScript.

→ Learn more about the algorithms used in this simulation

• T slider adjusts temperature of the simulation. Default value is the critical Temperature - approximately 2.269185 J/k (k=1 for this simulation)
• J slider adjusts the coupling constant between spins. The default value is 1.0. Positive J favors alignment (ferromagnetic) while negative J favors anti-alignment (antiferromagnetic).
• h slider adjusts the external magnetic field applied to the system. The default value is 0.0. Positive h favors +1 spins while negative h favors -1 spins.
• The sweeps per frame slider allows users to control how many Monte Carlo sweeps are performed between each frame update, affecting the speed of the simulation. The simulation speed is tied to the screen refresh rate, so it will be capped on monitors with lower refresh rates (typically 60Hz, 120Hz, or 144Hz). Making this value larger will speed up the simulation significantly since it will not have to render as often, but visually it will be less smooth, especially for larger lattices.
• Lattice size dropdown chooses size adjustment from 8x8 to 512x512
• Plot dropdown chooses which quantity to plot over time: average energy per site, average magnetization per site, or disable the plot entirely.
• Reset button reinitializes the lattice with random spins and resets the simulation statistics.

The Ising model is a mathematical model of ferromagnetism in statistical mechanics. It consists of discrete variables that represent magnetic dipole moments of atomic spins, which can be in one of two states (+1 or −1). The model helps to understand phase transitions and critical phenomena in physics.