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Bachelor Thesis from the year 2010 in the subject Physics - Theoretical Physics, grade: 1,3, University of Frankfurt (Main) (Institut für theoretische Physik), language: English, abstract: 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.