Optimum Monte Carlo simulations: Some exact results
Journal of Physics A: Mathematical and General
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 obtain an accurate description for the relaxation time.
Talbot, J., Tarjus, G., & Viot, P. (2003). Optimum Monte Carlo simulations: Some exact results. Journal of Physics A: Mathematical and General, 36 (34), 9009-9023. https://doi.org/10.1088/0305-4470/36/34/305