Bazavov_BiasedMC

Bazavov_BiasedMC - Biased Metropolis-Heatbath Algorithm...

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Unformatted text preview: Biased Metropolis-Heatbath Algorithm Alexei Bazavov Florida State University November 2005 Introduction In the Metropolis procedure transition probability from the configuration ( k ) to ( l ) is given as W ( l )( k ) = f ( l, k ) w ( l )( k ) for l 6 = k W ( k ) ( k ) = f ( k, k ) + X l 6 = k f ( l, k )(1- w ( l )( k ) ) For the case of the non-symmetric proposal probabilities f ( l, k ) 6 = f ( k, l ) the acceptance probability can be modified as [Hastings (1970)] w ( l )( k ) b = min 1 , P ( l ) B P ( k ) B f ( k, l ) f ( l, k ) 1 Example: U (1) Lattice Gauge Theory Variables are complex numbers of unit length: U = e iφ , φ ∈ [0 , 2 π ) The problem is reduced to sampling the probability density (PDF) P α ( φ ) = N α e α cos φ where α is a parameter associated to the interaction of the link being updated with its environment. The corresponding cumulative distribution function (CDF) is F α ( φ ) = N α Z φ dφ e α cos φ where N α ensures the normalization F α (2 π ) = 1....
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Bazavov_BiasedMC - Biased Metropolis-Heatbath Algorithm...

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