  We study a kinetically constrained Ising process (KCIP) associated with a
graph G and density parameter p; this process is an interacting particle system
with state space $\{0,1\}^{G}$. The stationary distribution of the KCIP Markov
chain is the Binomial($|G|, p$) distribution on the number of particles,
conditioned on having at least one particle. The `constraint' in the name of
the process refers to the rule that a vertex cannot change its state unless it
has at least one neighbour in state `1'. The KCIP has been proposed by
statistical physicists as a model for the glass transition, and more recently
as a simple algorithm for data storage in computer networks. In this note, we
study the mixing time of this process on the torus $G = \mathbb{Z}_{L}^{d}$, $d
\geq 3$, in the low-density regime $p = \frac{c}{n}$ for arbitrary $0 < c < 1$;
this regime is the subject of a conjecture of Aldous and is natural in the
context of computer networks. Our results provide a counterexample to Aldous'
conjecture, suggest a natural modifcation of the conjecture, and show that this
modifcation is correct up to logarithmic factors. The methods developed in this
paper also provide a strategy for tackling Aldous' conjecture for other graphs.
