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

Giovanni Ossola·Alan D. Sokal
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Abstract

We show that linear congruential pseudo-random-number generators can cause systematic 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 random number is used per bond. These systematic errors arise from correlations within a single bond-update half-sweep. The errors can be eliminated (or at least radically reduced) by updating the bonds in a random order or in an aperiodic manner. It also helps to use a generator of large modulus (e.g. 60 or more bits).

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Giovanni Ossola, Alan D. Sokal. 2004-03-08. Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning. https://doi.org/10.1103/physreve.70.027701

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