Ferrenberg-Swendsen Reweighting and WHAM

A brief sketch of the derivation of the WHAM equations follows we note that a detailed explanation is available in the book by Frenkel and Smit [14], Consider the canonical reweighing (3.5). Our goal will be to combine the histograms pi(U) from several runs at different temperatures T to predict the distribution of potential energies at a new temperature T. Individually, each run enables us to reweight its histogram to obtain the distribution at T 

V is vector notation for the set of all component energies Vy, and A, j gives the coefficient of Vy in the ith run. The Ay, without subscript i, indicate the values of A in the target ensemble. The histograms collected in the runs are multidimensional in that they are tabulated as functions of the component energies as well as the order parameter . Similarly, the final result of the WHAM calculation is a multidimensional probability distribution in V J and . 

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