A spin glass on a square lattice using the Ising model refers to a disordered magnetic system where the magnetic moments (spins), arranged on a two-dimensional square lattice, interact with each other according to the rules of the Ising model. However, the key characteristic of a spin glass is the disorder in these interactions.

🧠Simulation

To simulate a spin glass on a square lattice, we can create a Python program using the Ising model. This model will feature spins arranged on a 2D lattice with random interactions (ferromagnetic or antiferromagnetic). The Metropolis algorithm is commonly used to simulate the system's evolution toward equilibrium.

Here’s an outline of the simulation:

1. Define the lattice size and initialize spins randomly.
2. Assign random interaction strengths (J) between neighboring spins.
3. Implement the Hamiltonian to calculate the system's energy.
4. Use the Metropolis algorithm to update spins based on temperature (T).
5. Run the simulation over a set number of steps and visualize the results.

Below is a Python implementation of the spin glass simulation:

https://gist.github.com/viadean/68d922fb3f1eb897ef937c40b8cd1d35

Features of This Simulation:

1. Lattice Initialization: Spins are randomly assigned (+1) or (-1).
2. Interaction Strengths: Random values ((+1) or (-1)) create frustration.
3. Energy Calculation: The Hamiltonian includes all nearest-neighbor interactions.
4. Metropolis Algorithm: Governs spin flips based on temperature (T).
5. Visualization: Displays the lattice and plots energy over time.

How to Run:

1. Save this script as spin_glass_simulation.py.
2. Install numpy and matplotlib if not already installed: pip install numpy matplotlib.