Improving Random Number Generators in the Monte Carlo simulations via twisting and combining

Problems for various random number generators accompanying the Wolff algorithm [U. Wolff, Phys. Rev. Lett. 62 (1989) 361; U. Wolff, Phys. Lett. B 228 (1989) 379] are discussed, including the hidden errors first reported in [A.M. Ferrenberg, D.P. Landau, Y.J. Wong, Phys. Rev. Lett. 69 (1992) 3382]. A general (though simple) method of twisting and combining for improving the performance of these generators is proposed. Some recent generators motivated by such a twisting and combining method with extremely long period are discussed. The proposed method provides a novel and simple way to improve RNGs in its performance.