Monte Carlo simulations of the Ising model

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.

Michael Adler is in the Department of Social Policy, University of Edinburgh.