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\centerline{\bfbigger Empirical relations between static and dynamic} 
\centerline{\bfbigger exponents for Ising model cluster algorithms} 
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\centerline{\big Paul D. Coddington}
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\centerline{\it Physics Department, Syracuse University, Syracuse NY 13244, U.S.A.}
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\centerline{\big Clive F. Baillie} 
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\centerline{\it Physics Department, University of Colorado, Boulder CO 80309, U.S.A.}
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% \centerline{September 1991}
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\centerline{\bf Abstract}
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\noindent
We have measured the autocorrelations for the Swendsen-Wang and the Wolff 
cluster update algorithms for the Ising model in 2, 3 and 4 dimensions.
The data for the Wolff algorithm suggest that the autocorrelations are
linearly related to the specific heat, in which case the dynamical critical 
exponent ${z_{int,E}^{W} = \alpha / \nu}$.
For the Swendsen-Wang algorithm, scaling the autocorrelations by the
average maximum cluster size gives either a constant or a logarithm,
which implies that ${z_{int,E}^{SW} = \beta / \nu}$ for the Ising model.

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\noindent
PACS numbers 05.50.+q, 11.15.Ha, 64.60.Ht.
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