  This discussion serves as an introduction to the use of Monte Carlo
simulations as a useful way to evaluate the observables of a ferromagnet. Key
background is given about the relevance and effectiveness of this stochastic
approach and in particular the applicability of the Metropolis-Hastings
algorithm. Importantly the potentially devastating effects of spontaneous
magnetization are highlighted and a means to avert this is examined.
  An Ising model is introduced and used to investigate the properties of a two
dimensional ferromagnet with respect to its magnetization and energy at varying
temperatures. The observables are calculated and a phase transition at a
critical temperature is also illustrated and evaluated. Lastly a finite size
scaling analysis is undertaken to determine the critical exponents and the
Curie temperature is calculated using a ratio of cumulants with differing
lattice sizes. The results obtained from the simulation are compared to exact
calculations to endorse the validity of this numerical process. A copy of the
code used, written in C++, is enclosed and is freely available for use and
modification under the General Public License.
