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:
- Phys. Rev. Lett. 117, 097601 (2016)
- Phys. Rev. B 97, 144104 (2018)
- 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:
- install anaconda by downloading from here and upload it to your directory.
- using queue system to install anaconda by
chmod 755 anaconda*.sh && ./anaconda*.sh
- install
numpy
,h5py
andmpi4py
by download them from here upload them as well. - 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.
- Download the script:
wget https://github.com/Chengcheng-Xiao/mpiPyMC/blob/master/MC_MPI*.py
- give correct permission:
chmod 755 MC_MPI*.py
- 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:
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.
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
:
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 |
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
- Add total energy plot, specific heat plot and susceptibility plot function for
MC_MPI.py
. - Better MPI implementation with respect to CPU number, or use OpenMP?
- Snap shot of specified one (or several) MC step(s).
- Hysteresis.
This project is licensed under the MIT License - see the LICENSE.md for details