Optimized replica gas estimation of absolute integrals and partition functions

Details Optimized replica gas estimation of absolute integrals and partition functions Optimized replica gas estimation of absolute integrals and partition functions

2010-02-03

arxiv.org/abs/1002.0861v1

Phys. Rev. E 82, 031132 (2010)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 2 figures

Scientific paper

10.1103/PhysRevE.82.031132

In contrast with most Monte Carlo integration algorithms, which are used to estimate ratios, the replica gas identities recently introduced by Adib enable the estimation of absolute integrals and partition functions using multiple copies of a system and normalized transition functions. Here, an optimized form is presented. After generalizing a replica gas identity with an arbitrary weighting function, we obtain a functional form that has the minimal asymptotic variance for samples from two replicas and is provably good for a larger number. This equation is demonstrated to improve the convergence of partition function estimates in a 2D Ising model.

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