Projects for the lecture Numerical Methods of Statistical Physics

The lecture was held by Markus Quandt and Giuseppe Burgio in summer term 2020 at University of Tübingen.

The used language for simulations is C++20. The IDE is CLion. The used build-system is Debian Buster. It should also work on other platforms with small modifications in CMakeLists.txt.

Testing different random-number-generators (RNGs)

I did a pi-Test with 2 different random number generators (RNGs). The program can run in a fully parallelized mode.

The RNGs were used from standard C++ header Random.h.

We can see the convergence of the Mersenne-Twister MT19937 algorithm with up to 1E10 random numbers per calculated point. Convergence doesn't seem to slow down until 1E10, so I assume we can calculate pi more exactly with more time. The maximum period of random numbers of MT19937 is pow(2,19937)-1, so this would be a thinkable limit.

The linear congruential RNG (LCG) is limited in randomness and periodicity which results in limited convergence. With this RNG it is not possible to determine pi more exactly than up to 1E-2.

Forest Fire Simulations

There are some interesting Simulations of Forest-Fire-Cellular-Automatons:

https://people.sc.fsu.edu/~jburkardt/c_src/forest_fire_simulation/forest_fire_simulation.html

https://perso.u-cergy.fr/~ahonecker/bs/software/forest2d.html

Sand Piles

This project is available under: https://github.com/Babalion/sandpiles

Calculate spectral dimensions of fractal structures

This project is available under: https://github.com/Babalion/Fractal-Dimensions

Solve the travelling-salesman-problem (tsp) with a simulated annealing algorithm

This project is available under: https://github.com/Babalion/simulated-annealing-tsp

Ising Model

2 Level System

This project is available under: https://github.com/Babalion/Ising2level

Sigma-Model

This is an Ising-Spin-System on a square lattice where every spin can direct in an arbitrary angle in 2D. One can thus parametrize each spin via angle theta. You can also view the simulation live via openCV. Example below:

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Babalion/NumericalMethodsInStatisticalPhysics