Inter-Faculty Ph D course, "Introduction to Monte Carlo methods in statistical physics" @ University of Parma, 2016.

Programme [3 hours per topic]

1. Numerical sampling and integration with random numbers
2. Markov-Chain Monte Carlo: exponential and integrated correlation times
3. Metropolis and heatbath (Gibbs sampling) algorithms
4. The Fortuin-Kasteleyn representation, cluster (Wolff and Swendseng-Wang) algorithms
5. Monte Carlo algorithms in different ensembles
6. Error estimation: estimators of the correlation, the Jack-knife method for correlated and uncorrelated data
7. Elements of parallel computing and general purpose Graphics Processing Units (GPGPU) computing
8. Parallel Monte Carlo algorithms
9. Elements of Markov-Chain Monte Carlo in Bayesian inference
10. Elements of Finite Size Scaling theory
11. Finite size effects in first-order transitions and in the Kosterlitz-Thouless transition.

The material:

Find here the lecture notes.

Auxiliary preliminar material: Crash course on statistical physics .

Code sources, scripts and libraries . Contain: the code sources (mainly in C++ and python) implementing most of the algorithms discussed in the course, and used to generate the lecture examples and exercises; a list of GPGPU computing examples in CUDA language; a list of useful and self-explaining scritps dedicated to data processing and visialization (as python scripts computing jackknife errors and correlation functions/times of general data).