Physical Tests for Random Numbers in Simulations

We propose three physical tests to measure correlations in random num-bers used in Monte Carlo simulations. The rst test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wol 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 simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences. We also determine the length of these correlations. PACS numbers: 02.70.Lq, 75.40Mg, 05.40+j, 05.50.+q. The Monte Carlo (MC) simulation method is a standard technique in physical sciences [1]. The key ingredient in its successful application lies in the quality of random numbers used, which are usually produced by deter-ministic pseudorandom number (PRN) generator algorithms. Several tests for PRN generators have been suggested [2, 3, 4] and conducted [3, 4, 5, 6