Phase transitions in the Ising model with random gap defects using the Monte Carlo method
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The Ising model, the simplest model of ferromagnetism, describes a magnetic lattice with nearest-neighbor interactions and is governed by Boltzmann statistics. The Monte Carlo method provides one approach to simulate thermal fluctuations in the Ising Model using a stochastic process to randomly determine dipole-dipole interactions. This allows the Ising model to predict the equilibrium state of a lattice for a given temperature. I estimate the Curie temperature in the two-dimensional zero field Ising model using the Monte Carlo method to be 2.465 +/- 0.052. In a real material, however, neighboring dipoles are not always perfect; defects can occur within the substance. I define a defect to be the absence of a dipole at a random point in the lattice. In this thesis, I determine the expected dependence of the Curie temperature on defect density in the two-dimensional Ising model.
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