Ising Model Simulation

Dependencies

• You should have some version of python 3.x with numpy, matplotlib, numba, and multiprocessing installed.
  • If you don't have these, you can always pip install --user package_name or add them to a conda environment.

Simulation

• To simulate, run python simulate.py.

  • The default simulation will run for L = [10, 16, 24, 36] and 300 temperature points between 0.015 and 4.5.
  • The computationally heavy functions (i.e. energy(), magnetization(), and mc_step_metropolis() are all either vectorized or compiled just-in-time with numba.
  • The code should also detect how many CPU cores your computer has available and parallelize the calculation for each temperatue.
  • Without parallelization, the entire calculation (on an older Nevis computer) takes ~8-9 hrs. On my MacBook Pro with parallelization to 12 cores, I estimate it should take ~30-45 mins.

• The simulation will store the results for each lattice size L as structured arrays on .npy files under ./data.

  • These should contain data for E, M, C, Chi, and T that are easy to read-in and plot.

Analysis

• To make plots, run python analysis.py.
  • This will generate plots under ./plots.
  • These include plots of the energy, magnetization, heat capacity, susceptibility, critical temperatures, etc.

If you want to run your own analysis

• You can read-in the saved structured arrays by just replacing X below with the desired system size:

import numpy as np

with open("./path_to_data/ising_2d_L_X.npy", "rb") as f:
  array = np.load(f)

• You can then access the data from these arrays as T = array["T"] or Chi = array["Chi"] and run your own scripts.

Note

I still need to finish fleshing out the analysis and writing some documentation for it, so just use it with this in mind!