This repository contains the code and thesis for my bachelor project in physics.
The focus of the project is the thermodynamic behaviour and the phase transition of the 3-state Potts model (a generalization of the Ising model). The partition function of this system can not be exactly determined. Therefore numerical approaches using Monte Carlo methods are employed. Using finite size scaling methods the critical temperature and critical exponents are found.
You can play with the simulations yourself. The required Python 3 packages are
- Matplotlib
- Scipy
- Numpy
- Cython
- Seaborn
You also need a C compiler.
To run a simulation yourself:
make # Build the Cython extensions
# Run a simulation of the Ising model through the command line
python3 ./simulation.py ising wolff 10 20 1 hi 5000 16384 2 3The iPython notebooks ising.ipynb and potts.ipynb can be run to determine the critical temperature and critical exponents of the respective models. You can just do run all.
The required datasets are included in the repository.
python3 ./simulation.py -h
usage: simulation.py [-h] [--step STEP] [--show_plots] [--nosave]
{ising,potts} {metropolis,wolff} lattice_sizes
[lattice_sizes ...] bond_energy {hi,lo}
thermalization_sweeps measurement_sweeps lower upper
Simulate the 2- and 3-state Potts model in 2D.
positional arguments:
{ising,potts} Either Ising (q=2) or Potts (q=3)
{metropolis,wolff} Algorithm to use for simulation
lattice_sizes Lattice sizes to simulate
bond_energy Specify the bond energy
{hi,lo} specify initial temperature of simulation ("hi" is
infinite, "lo" is 0)
thermalization_sweeps
Number of sweeps to perform before measurements start
measurement_sweeps Number of sweeps to measure
lower Lower temperature bound
upper Upper temperature bound
optional arguments:
-h, --help show this help message and exit
--step STEP Temperature step, default is 0.2
--show_plots Show plots on error calculations, default is false
because this is a blocking operation
--nosave Do not save output in a binary pickle file, default
behaviour is that it is saved