PHYSICAL MODELS AS TESTS OF RANDOMNESS

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.