The flat histogram Monte Carlo (FHMC) algorithm has been proposed as an efficient sampling scheme for problems with a complex free energy landscape. Its successful implementation requires fast and stable determination of the sampling weight function which can be a challenge for simulation at low temperatures. We describe here a polynomial parameterization of the sampling weight function which allows one to perform noise filtering and extrapolation at the same time. Efficiency of the scheme as compared to Berg's original iterative formula is demonstrated on the two-dimensional compass model for d-orbital ordering.
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