mpiPyMC

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)

Getting Started

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

Prerequisites

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

Installing

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).

Adjustable spin (polarization vector)

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.

Input File

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

FOR MC_MPI.py:

NAME	DEFAULT	MEANING
nt	18	[number of Temperature point, should be integer number of the CPU used]
N	16	[number of cell in onedirection, total number of cell =N*N]
eqSteps	2000	[number of MC steps to get to equilibrium]
mcSteps	2000	[number of MC steps to use for average]
A_data	-8.021	[model data]
B_data	0.620	[model data]
C_data	0.441	[model data]
D_data	4.5	[model data]
ps	1.867	[spontaneous polarization value]
T_low	0.01	[temperature range]
T_high	300	[temperature range]

FOR MC_MPI_Ising.py:

NAME	DEFAULT	MEANING
nt	18	[number of Temperature point, should be integer number of the CPU used]
N	16	[number of cell in onedirection, total number of cell =N*N]
eqSteps	8000	[number of MC steps to get to equilibrium]
mcSteps	4000	[number of MC steps to use for average]
D_data	1.0	[model data]
T_low	1.53	[temperature range] assuming K_b=1
T_high	3.28	[temperature range] assuming K_b=1

Output

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

Example

MC_MPI example

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.

MC_MPI_Ising example

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

Note

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

Future development plan

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.

License

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