A python based, MPI enabled, Monte-Carlo calculation of 2D Ising system using Metropolis algorithm.

Before getting into things, you might want to check out these papers:

1. Phys. Rev. Lett. 117, 097601 (2016)
2. Phys. Rev. B 97, 144104 (2018)
3. Appl. Phys. Lett. 111, 132904 (2017)

These instructions will get you a copy of the project up and running on your machine.

For the script to work, you need to have an valid installation of python (2.7.x or 3.x both work), and a MPI installation:

openmpi:https://www.open-mpi.org/
MPICH:https://www.mpich.org/
intelmpi:https://software.intel.com/en-us/mpi-library

Also, numpy, matplotlib, tqdm and mpi4py package are needed, you can install them by pip:

pip install matplotlib numpy mpi4py tqdm

or by conda

conda install matplotlib numpy mpi4py tqdm

if you use a supercomputer and don't have enough privilege:

1. install anaconda by downloading from here and upload it to your directory.
2. using queue system to install anaconda by chmod 755 anaconda*.sh && ./anaconda*.sh
3. install numpy, h5py and mpi4py by download them from here upload them as well.
4. manually install package by conda install *package_name*.tar.bz2

Version of dependencies tested:

• python = 3.8
• matplotlib = 3.5.0
• numpy = 1.21.2
• mpi4py = 3.0.3
• tqdm = 4.62.3

Python script does not need manual compilation, so the installation is very easy.

1. Download the script:

wget https://github.com/Chengcheng-Xiao/mpiPyMC/blob/master/MC_MPI*.py

2. give correct permission:

chmod 755 MC_MPI*.py

3. change parameters inside the code and run it by:

mpirun -np XX MC_MPI*.py

XX is for number of processes (please keep XX <= the number of temperature points+1).

This project provide two different script for two different tasks:

1. MC_MPI.py: for adjustable spin. Utilize Sigma^4 Model:

E=∑[(A/2)*P_i^2+(B/4)*P_i^4+(C/6)*P_i^6]+∑[(D/2)*(P_i-<P_j>)^2]

where i and j are nearest neighbor.

2. MC_MPI_Ising.py: for spin = +1 or -1. Utilize Heisenberg Model:

E=∑[(D)*P_i*P_j]

where i and j are nearest neighbor.

All adjustable variables should be written in input.MC file.

FOR MC_MPI.py:

FOR MC_MPI_Ising.py:

MC_MPI.py will output picture MC.png and data Polarization.txt, containing Polarization vs Temperature plot and the raw data to generate the plot, respectively.

MC_MPI_Ising.py will output picture MC.png containing total energy plot, specific heat plot, susceptibility plot and Polarization vs Temperature plot. as well as their raw data Energy.txt, Polarization.txt, Specific_Heat.txt, Susceptibility.txt

In the example folder, I have included three examples for mentioned reference papers. The systems are: SnSe, ß-GeSe, SnTe and GeTe.

I was not able to reproduce the result for SnSe and ß-GeSe. The calculated results forSnTe and GeTe agree with said paper.

Analysis of possible errors are presented inside each folder separately. In short, the definition of nearest neighbor is very important. However, no explanations were made in these referenced paper. The coupling coefficient D should be calculated via changing one cell's polarization in a supercell configuration. The coupling plot should be calculated by subtracting the site energy from the total energy.

In the example_Ising folder, I have included three calculations of Ising model. each with different cell size: 16X16, 30X30 and 50X50.

This code is based on rajeshrinet's work: 🔗LINK

1. Add total energy plot, specific heat plot and susceptibility plot function for MC_MPI.py.
2. Better MPI implementation with respect to CPU number, or use OpenMP?
3. Snap shot of specified one (or several) MC step(s).
4. Hysteresis.

This project is licensed under the MIT License - see the LICENSE.md for details