The most important computer simulation methods in condensed matter physics are presented and applied to specific exercises. Each student is asked to write down the simulation codes for these exercises and to analyze the outcome of the simulations.
lectures and programming sessions.
Generalities on computer simulations. Monte Carlo Method - Simple sampling and importance sampling. Markov chains. Conditions for convergence at equilibrium. Detailed balance. Metropolis algorithm. Monte Carlo step. Application to the two-dimensional lattice gas on a square lattice. Order Parameter. Order-disorder phase transitions. Continuous time Monte Carlo. Application to the growth of islands in two dimensions. Mean field theory for island counting. Fractal dimension. Molecular Dynamics - Structure of a classical Molecular Dynamics program. Microcanonical simulations. Preparing the initial configuration. Algorithms for propagating the trajectories. Euler algorithm. Verlet algorithm. Leapfrog and velocity verlet algorithms. Canonical simulations. Andersen Thermostat. Simulation of a cluster of argon atoms.
Lecture notes
