Statistical Mechanics: Algorithms and Computations

This module introduces Monte Carlo algorithms, including direct sampling and Markov-chain sampling. It covers the essential concepts of Monte Carlo techniques and the Metropolis algorithm.

This module covers the hard-disk model, comparing direct sampling and Markov-chain sampling, and exploring the connection between Monte Carlo and Molecular Dynamics algorithms.

This module introduces entropic interactions using a clothe-pins model and explores phase transitions. It also covers the connection between exact solutions and perfect sampling algorithms.

This module deepens the understanding of sampling and its connection with integration, introducing Maxwell and Boltzmann distributions. It also covers high-dimensional integration techniques.

This module introduces quantum statistical mechanics, covering density matrices, path integrals, and the Trotter approximation. It also includes matrix-squaring techniques and anharmonic potential studies.

This module covers bosons and their statistics, introducing the Lévy construction sampling algorithm. It compares this algorithm with standard sampling techniques.

This module discusses Bose-Einstein condensation, describing the phenomenon using permutation cycles in the path-integral framework. It also introduces a sampling algorithm based on this concept.

This module introduces the Ising model and various sampling algorithms for it, including local algorithms, cluster algorithms, and the heat-bath algorithm. It also covers coupling of Markov chains.

This module covers dynamic Monte Carlo algorithms, including the faster-than-the-clock approach. It also introduces simulated annealing and its applications to optimization problems.

This final module covers Buffon's needle experiment and Lévy stable distributions. It includes a review of the entire course material.