Mats Wallin

These lecture notes give a simple introduction to some main ideas and techniques used in Monte Carlo simulations. Both the principles and practicalities are discussed. The aim is to use simulations as an quick and eective tool to obtain nontrivial information in dicult problems, where solution with other methods may be dicult or impossible. The focus is on applications in statistical physics. Examples such as spin models in classical statistical physics, and harmonic oscillators in quantum mechanics are explained in some de-tail. Various advanced techniques like nite size scaling and collective updating algorithms are considered, which can vastly improve performance of the simulation. Some orientation on open problems will be given. These lecture notes are for a fourth year undergraduate course on computational physics. As-sumed prerequisites are basic statistical mechanics and quantum mechanics. Elementary pro-gramming skills are assumed, preferably in a compiling language like FORTRAN of C, since interpreting languages are often too slow for simulations. Simulation is best learned by simulation. A set of study projects accompany this text, and problems are included throughout the text. For more details on the subject some of the excellent textbooks in the reference list should be consulted. Please report suggestions, comments, an