2D Ising Model Simulation

Real-time visualization of ferromagnetic domain formation near the critical temperature.

Overview

This project is a Python-based Monte Carlo simulation of the 2D Ising Model, a mathematical model of ferromagnetism in statistical mechanics. It uses the Metropolis-Hastings algorithm to simulate magnetic spin dynamics on a lattice.

I built this to explore phase transitions, specifically how macroscopic order (magnetism) emerges from microscopic interactions and how systems behave near the critical point.

Features

• Metropolis Dynamics: Implements the Metropolis-Hastings acceptance criterion for spin flips.
• Real-time Visualization: Uses matplotlib.animation to visualize spin evolution and domain growth.
• Periodic Boundary Conditions: Simulates an infinite lattice by wrapping grid edges.
• Customizable Parameters: Easy adjustment of Grid Size ($N$), Temperature ($T$), and Interaction Strength ($J$).

Usage

1. Prerequisites

You will need Python installed along with the following libraries:

pip install numpy matplotlib