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Evans, John Thomas

Electrical Engineering

2011

MS

A wavelet accelerated, Monte Carlo algorithm for simulation of the finite Ising Model is presented, based on a hierarchical decompoSition of the model using the discrete wavelet transform, employing the Haar wavelet. An empirically derived relationship between the temperature in the original model T and an optimal temperature of a decomposed model T is discovered for finite size Ising models at various decomposition levels. The optimal temperature relationship Monte Carlo (OTRMC) algorithm provides improved accuracy of estimates of thermodynamic quantities, especially in the critical and paramagnetic regions, as compared to previous methods, while greatly reducing the computational cost. Quantitative evidence is provided, suggesting that at each decomposition level, the optimal temperature relationships derived for the finite size Ising models converge with increasing lattice size. This suggests that large-size Ising models could be simulated using the optimal temperature relationships derived from small-size models, thereby allowing for inspection of models that are currently intractable.