Monte Carlo Methods applied to the Ising model

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.

Résumé
The thermodynamic observables of the classical one and twodimensional 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.

Contenu

1. Statistical mechanics -- a short review2. Monte Carlo simulation3. Selected resultsA. Source code of MC integratorsB Implementation of the Ising modelsBibliographyList of Figures