In this book the thermodynamic observables of the classical one- and two-dimensional
ferromagnetic and antiferromagnetic Ising models on a square lattice are simulated especially
at the phase transitions (if applicable) using the classical Monte Carlo algorithm of
Metropolis. Finite size effects and the influence of an external magnetic field are described.
The critical temperature of the 2d ferromagnetic Ising model is obtained using finite size
scaling. Before presenting the Ising model the basic concepts of statistical mechanics are
recapped. Furthermore the general principles of Monte Carlo methods are explained.
