🚀 go-pugleaf

In article <1993Jan13.002020.10338@Princeton.EDU> rdnelson@phoenix.Princeton.EDU (Roger D. Nelson) writes:
>>In article <dmurdoch.393.726873235@mast.queensu.ca> dmurdoch@mast.queensu.ca
>(Duncan Murdoch) writes:
>>>The paper is Ferrenberg, A. M., Landau, D.P., and Wong, Y.J. (1992), Monte 
>>>Carlo simulations:  hidden errors from "good" random number generators,
>>>Physical Review Letters 69 no. 23, 3382-3384.
>>
>>Oops, I forgot to mention:
>>
>>The authors did find that simple variations on the algorithms (e.g. only use 
>>every 5th random number) gave acceptable results.

>I must be missing something, for _this_ result suggest high-frequency
>autocorrelations that are eliminated by dumping the 2-4th elements.

I suspect something like this:  the Ising model simulations probably have a 
very strong periodicity in how they use the random numbers.  That "strains" 
the RNG at one particular frequency in its spectrum.  Something about the 
Wolff algorithm is very sensitive to any deviation from the white spectrum 
at that particular frequency.  The CONG generator just happened to do best 
at that frequency; the others were off by a bit.  When the Wolff algorithm 
amplified the problems, they showed up as errors in the mean in the 4th 
or 5th decimal place.

The "every 5th" solution was presented as though it was one of many things 
the authors tried (though I don't think they said this).  It may well just 
be chance that using every 5th number happens to bring the right spectral 
density to that critical spot.

I think they got the conclusions bang on:  you can't rely on standard tests 
to validate a RNG when you're going to use it in ten million repeated 
simulations.

Duncan Murdoch
dmurdoch@mast.queensu.ca