  The purpose of this article is to present a detailed numerical study of the
second-order phase transition in the 2D Ising model. The importance of
correctly presenting elementary theory of phase transitions, computational
algorithms and finite-size scaling techniques results in a important
understanding of both the Ising model and the second order phase transitions.
In doing so, Markov Chain Monte Carlo simulations are performed for different
lattice sizes with periodic boundary conditions. Energy, magnetization,
specific heat, magnetic susceptibility and the correlation function are
calculated and the critical exponents determined by finite-size scaling
techniques. The importance of the correlation length as the relevant parameter
in phase transitions is emphasized.
