Python Implementation of Ising model in 2D and 3D

Python code implementing Markov Chain Monte Carlo for 2D and 3D square-lattice Ising model.

• Numba JIT compiling supported
• Multiprocessing supported

Warning

Experiments for a large scale 3D-lattice Ising model consume a lot of energy and time. We strongly recommend you to use a server with decent multi-core CPUs.

Result

It is possible to calculate mean energy, magnetization, specific heat, and susceptibility at various temperatures and save it to a csv file and a plot.

We ran this code for 16000 equilibration steps and 16000 Monte Carlo steps on a 30 x 30 x 30 lattice to get the result above.

Install requirements

To install requirements, run the command below:

pip install -r requirements.txt

Options

Monte Carlo arguments

• size (default=30): Length of the lattice -> L
• dim (default=3): Dimension of the lattice -> D
• init_temp (default=1.5): Initial temperature -> T_0
• final_temp (default=6.5): Final temperature -> T_f
• temp_step (default=0.04): Temperature step -> dT
• eqstep (default=1000): Number of equilibration steps
• mcstep (default=1000): Number of Monte Carlo steps

Misc

• seed (default=0): Random seed
• n_proc (default=0): Number of processes for multiprocessing. If n_proc = 0, then use all CPU cores available
• no_record (default=record): Whether to record the result or not
• no_plot (default=plot): Whether to plot the result or not

Examples

To run experiments, run the command below:

2D-lattice Ising model

python main.py --size 30 --dim 2 --init_temp 1.5 --final_temp 3.5 --temp_step 0.02 --eqstep 1000 --mcstep 1000

3D-lattice Ising model

python main.py --size 30 --dim 3 --init_temp 1.5 --final_temp 6.5 --temp_step 0.04 --eqstep 3000 --mcstep 3000

Future works to be done

We want to parallelize the sampling procedure using GPU.

We also want to speed up the process using various techniques (e.g. importance sampling).

If you have abundant knowledge of those techniques, please contact us!