  Quantum spin systems are by now known to exhibit a large number of different
classes of spin liquid phases. By contrast, for \textit{classical} Heisenberg
models, only one kind of fractionalised spin liquid phase, the so-called
Coulomb or $U(1)$ spin liquid, has until recently been identified: this
exhibits algebraic spin correlations and impurity moments, `orphan spins',
whose size is a fraction of that of the underlying microscopic degrees of
freedom. Here, we present two Heisenberg models exhibiting fractionalisation in
combination with exponentially decaying correlations. These can be thought of
as a classical continuous spin version of a $\mathbb{Z}_2$ spin liquid. Our
work suggests a systematic search and classification of classical spin liquids
as a worthwhile endeavour.
