Monte Carlo Ising Model

This program simulates a simplified 2D Ising model with the Monte Carlo method. It uses NumPy to load a 2D spin lattice and Matplotlib to visualize the result. The program is also able to use PyCUDA for (optional) GPU acceleration.
NOTE: For small enough lattice dimensions and number of steps, computing on the GPU may seem slower due to host->device and device->host memory transfer.

In every step of the simulation, one spin is selected at random. Its energy is calculated with the given formula:

$$E_{i,j} = -s_{i,j}*(s_{i+1,j}+s_{i-1,j}+s_{i,j+1}+s_{i,j-1})$$

Where:

• i, j are the indexes of the spin's row and column, respectively

• s is the value of the given spin (either 1 or -1)

• E is the energy of the spin's square

If the calculated energy is greater than 0, the spin will switch. Otherwise, it will switch with the probability given by the following formula:

$$P(switch_{i,j})=e^{(2*E_{i,j})/T}$$

Where T is the systems temperature.

Installation:

First, clone the repository.

git clone https://github.com/Griger5/Monte_Carlo_Ising_Model.git

Then create and activate the virtual environment for the program.

python -m venv .venv

On Windows:

PowerShell:

Set-ExecutionPolicy -ExecutionPolicy RemoteSigned -Scope CurrentUser
.venv\Scripts\Activate.ps1

cmd:

.venv\Scripts\activate.bat

On Linux:

bash/zsh:

source .venv/bin/activate

csh/tcsh:

source .venv/bin/activate.csh

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After that is done, install all the required libraries using:

pip install -r requirements.txt

Usage

This program supports user command line arguments. When none are present, it will run with the default parameters listed below. If a GPU and CUDA drivers are detected, the simulation will run on the GPU. Otherwise it simply runs on the CPU.

Default parameters:

• Number of rows: 200
• Number of columns: 200
• Number of steps in the simulation: 10^6 (10^8 with GPU present)
• Temperature: 2.0
• Spin values: Initialized randomly

When in the virtual environment, you can run the program with:

python ising_model.py [--args n] [--flags]

Args:

--file [filepath]

Loads the lattice from a file. The file should contain a flattened lattice (as in: '1 -1 1 -1 1 1 -1 1...'). If rows and columns are not specified by the user, the program will attempt to turn the loaded lattice into a square.

--rows [int]

Specify the number of rows for the spin lattice.

--cols [int]

Specify the number of columns for the spin lattice.

--steps [int]

Specify the number of Monte Carlo steps in the simulation.

--temp [double]

Specify the temperature for the simulation.

Flags:

--anim

When present, produces an animation of the simulation instead of a "before and after" image. GPU acceleration is not supported for creating an animation.

--no_gpu

When present, forces the program to compute on CPU.

Example run:

python ising_model.py --rows 150 --cols 150 --temp 1.75 --anim