Simulating graphene impurities using the worm algorithm

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The two-dimensional Ising model is studied by performing computer simulations with one of the Monte Carlo algorithms - the worm algorithm. The critical temperature TC of the phase transition is calculated by the usage of the critical exponents and the results are compared to the analytical result, giving a very high accuracy. We also show that the magnetic ordering of impurities distributed on a graphene sheet is possible, by simulating the properly constructed model using the worm algorithm. The value of TC is estimated. Furthermore, the dependence of TC on the interaction constants is explored. We outline how one can proceed in investigating this relation in the future.