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We show that linear congruential pseudo-random-number generators can causesystematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm,if the lattice size is a multiple of a very large power of 2 and one randomnumber is used per bond. These systematic errors arise from correlations withina single bond-update half-sweep. The errors can be eliminated (or at leastradically reduced) by updating the bonds in a random order or in an aperiodicmanner. It also helps to use a generator of large modulus (e.g. 60 or morebits).Comment: Revtex4, 4 page

Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning