Physical Tests for Random Numbers in Simulations

We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks and the third on blocks of $n$ successive numbers. We apply the tests to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences.