Optimum Monte Carlo Simulations: Some Exact Results

Details Optimum Monte Carlo Simulations: Some Exact Results Optimum Monte Carlo Simulations: Some Exact Results

2003-02-18

arxiv.org/abs/cond-mat/0302366v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, 8 figures. submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/36/34/305

We obtain exact results for the acceptance ratio and mean squared displacement in Monte Carlo simulations of the simple harmonic oscillator in $D$ dimensions. When the trial displacement is made uniformly in the radius, we demonstrate that the results are independent of the dimensionality of the space. We also study the dynamics of the process via a spectral analysis and we obtain an accurate description for the relaxation time.

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