I. Vattulainen et al., PHYSICAL MODELS AS TESTS OF RANDOMNESS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(3), 1995, pp. 3205-3214
We present and analyze in detail a test bench for random number sequen
ces based on the use of physical models. The first two tests, namely t
he cluster test and the autocorrelation test, are based on exactly kno
wn properties of the two-dimensional Ising model. The other two, the r
andom walk test and the n-block test, are based on random walks on lat
tices. We have applied these tests to a number of commonly used pseudo
random number generators. The cluster test is shown to be particularly
efficient in detecting periodic correlations on bit level, while the
autocorrelation, the random walk, and the n-block tests are very well
suited for studies of weak correlations in random number sequences. Ba
sed on the test results, we demonstrate the reasons behind errors in r
ecent high precision Monte Carlo simulations, and discuss how these co
uld be avoided.