*Abstract:*

The Swendsen-Wang process provides one possible dynamics for the
*Q*-state Potts model in statistical physics. Computer
simulations of this process are widely used to estimate the
expectations of various observables (random variables) of a Potts
system in the equilibrium (or Gibbs) distribution. The legitimacy
of such simulations depends on the rate of convergence of the
process to equilibrium, often known as the mixing rate. Empirical
observations suggest that the Swendsen-Wang process mixes rapidly
in many instances of practical interest. In spite of this, we show
that there are occasions on which the Swendsen-Wang process
requires exponential time (in the size of the system) to approach
equilibrium.

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