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J. Phys. Condens. Matter (in Press)
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17
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85034292049
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note
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8 steps were divided into 50-100 blocks. With blocks of this size a further increase of the block size did not affect estimates of the standard deviations of the averages.
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85034310465
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note
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In principle, one could cover the whole density range of interest in a single Monte Carlo run, but to speed the computations, the initial density interval can be divided into subintervals (Ref. 4). Indeed, due to the diffusive nature of MC sampling, the computation time necessary to cover some density interval grows eventually as the square of the interval length. Therefore, the time required to cover two large density intervals in two different runs is only two times larger then the time required for one interval, while performing a single run covering the doubled interval would require four times the computation time. However, it is not reasonable to use many very small density intervals, since every density "seam," where these intervals must be matched together, introduces some extra errors into the resulting values of the relative excess free energies.
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26
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85034282914
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note
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Generally, one can use different grids in calculations of the sampling function and of the relative excess free energy (Ref. 4). In the present study we use the same grid for both calculations.
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27
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0003556247
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28
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85034300009
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note
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i,j are given in Table II.
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29
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85034307214
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note
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In practice we found by least squares an additive constant that matched the TDSMC data of the small near-critical temperature-density window to the 5656-fit previously obtained for the rest of the data.
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31
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