We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties. The histogram method also allows us to directly obtain an estimate of the interior radial probability density profile, thus yielding useful insight into the structural properties of such a high-dimensional body. We illustrate the method by analyzing the effect of structural disorder on the basins of attraction of mechanically stable packings of soft repulsive spheres.
Bibliographical noteFunding Information:
S.M. acknowledges financial support by the Gates Cambridge Scholarship. K.J.S. acknowledges support by the Swiss National Science Foundation under Grants No. P2EZP2-152188 and No. P300P2-161078. J.D.S. acknowledges support by Marie Curie Grant No. 275544. D.F. and D.J.W. acknowledge support by EPSRC Programme Grant No. EP/I001352/1, by EPSRC Grant No. EP/I000844/1 (D.F.) and ERC Advanced Grant No. RG59508 (D.J.W.)
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