Markov Chain Monte Carlo Methods in Percolation

Union College research fellowship, summer 2008
Advisor: Prof. Gary Reich

The mathematical theory of percolation can be used to describe a variety of phenomena. Permanent magnets are a prominent example - when they are heated beyond a certain temperature (the Curre point), they become demagnetized, and this demagnetization can be modeled by percolation theory. However, the critical parameters given by this theory, the “critical exponents”, are difficult to compute. But it is hoped that using a random sampling method based on a Markov chain Monte Carlo simulation can help us give reasonable estimates. This project was a preliminary investigation into this method’s feasibility.

• Final report [pdf]
• Data, programs, source files [zip]

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