2D Ising Model using the Metropolis Algorithm

Overview

This is a simulation of the 2D Ising model using the Metropolis algorithm, a Monte Carlo method for modeling the behavior of ferromagnetic materials and phase transitions in statistical physics. It displays the evolution of spin configurations on a 2D lattice, as well as the energy, magnetization, and energy histogram over time.

The simulation is interactive, featuring a reset button to reinitialize the model and observe different random configurations.

Features

• 2D Ising spin lattice: Each site on an N*N grid contains a spin (+1 or -1).
• Metropolis algorithm for Monte Carlo updates:
  • Randomly selects lattice points and probabilistically flips spins.
  • Considers change in energy and temperature for acceptance of spin flips.

How It Works

• Lattice Initialization: The system starts with a random $$N \times N$$ lattice of spins, each set to +1 or -1.
• Energy Calculation: The energy considers nearest-neighbor spin interactions and periodic boundary conditions.
• Metropolis Algorithm: For each Monte Carlo step:
  • Randomly select a site.
  • Compute the energy change if the spin is flipped.
  • Flip the spin with a probability determined by the Boltzmann factor $$\exp(-\Delta E / T)$$.
• Measurements:
  • Energy: Calculated by summing over all pairs of neighbors.
  • Magnetization: Sum of all spins in the lattice.

Usage

1. Clone the repository:

   git clone https://github.com/AakaashfromIndia/2D-Ising-model-using-Metropolis-Algorithm.git

2. Install dependencies:

   pip install numpy matplotlib

3. Run the simulation:

   python Ising-Model.py

4. Use the Reset button in the GUI to start with a new random configuration.

Dependencies

• Python 3.x
• NumPy
• Matplotlib