Simulation of the Ising model on a square lattice with the Metropolis algorithm, which is a Markov chain Monte Carlo method for sampling the equilibrium distribution of a system. In addition to pure Python implementation (ising.py), the code is also implemented with Numba (ising_numba.py) and in Cython (ising_cython.pyx). The Cython code is parallelized with OpenMP.
The simulation can be simply run with python driver.py. One can change the parameter values therein.
Should any modifications be made to ising_cython.pyx, one would need to to run python setup.py build_ext --inplace in a CIL to re-compile it to C. Then the function run_ising_cython(...) can be imported in any Python script (see e.g., driver.py).
Here's a plot showing the evolution of energy and magnetization expectations with temperature for different system sizes (L = 10, 20, 40, 80).
Another plot showing the performance/speed gain using Numba and Cython, normalized to the pure Python implementation, for different system sizes (L = 2, 4, 6, 8, 10, 12):
Here is a GIF showing the evolution of the spin configuration (80 x 80) as temperature increases:
