  In this paper we consider the algorithmic problem of sampling from the Potts
model and computing its partition function at low temperatures. Instead of
directly working with spin configurations, we consider the equivalent problem
of sampling flows. We show, using path coupling, that a simple and natural
Markov chain on the set of flows is rapidly mixing. As a result we find a
$\delta$-approximate sampling algorithm for the Potts model at low enough
temperatures, whose running time is bounded by $O(m^2\log(m\delta^{-1}))$ for
graphs $G$ with $m$ edges.
