PHYSICAL MODELS AS TESTS OF RANDOMNESS

We present and analyze in detail a test bench for random number sequences based on the use of physical models. The first two tests, namely the cluster test and the autocorrelation test, are based on exactly known properties of the two-dimensional Ising model. The other two, the random walk test and the n-block test, are based on random walks on lattices. We have applied these tests to a number of commonly used pseudorandom 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. Based on the test results, we demonstrate the reasons behind errors in recent high precision Monte Carlo simulations, and discuss how these could be avoided.