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We report large systematic errors in Monte Carlo simulations of thetricritical Blume-Capel model using single spin Metropolis updating. The error,manifest as a $20\%$ asymmetry in the magnetisation distribution, is traced tothe interplay between strong triplet correlations in the shift register randomnumber generator and the large tricritical clusters. The effect of thesecorrelations is visible only when the system volume is a multiple of the randomnumber generator lag parameter. No such effects are observed in related models.

ERRORS IN MONTE CARLO SIMULATIONS USING SHIFT REGISTER RANDOM NUMBER GENERATORS