  Tau leaping is a popular method for performing fast approximate simulation of
certain continuous time Markov chain models typically found in chemistry and
biochemistry. This method is known to perform well when the transition rates
satisfy some form of scaling behaviour. In a similar spirit to tau leaping, we
propose a new method for approximate simulation of spin systems which
approximates the evolution of spin at each site between sampling epochs as an
independent two-state Markov chain. When combined with fast summation methods,
our method offers considerable improvement in speed over the standard
Doob-Gillespie algorithm. We provide a detailed analysis of the error incurred
for both the number of sites incorrectly labelled and for linear functions of
the state.
