  Frustrated magnets typically possess a large space of classical ground
states. If this degeneracy is not protected by symmetry, thermal fluctuations
may `select' certain states via order-by-disorder. In this article, we examine
a precursor effect where all ground states are sampled, but with different
weights. Geometry plays a key role in determining the weight distribution and
its behaviour. We demonstrate this with two examples -- both clusters with four
spins coupled by XY interactions. In the first, the classical ground states
form a smooth space. In the second, they form a self-intersecting non-manifold
space. Ground state sampling is very different in these two cases. We first
consider the microcanonical ensemble picture, where fluctuations conserve
energy. Phase space arguments suggest that the first model exhibits
energy-independent probabilities. The second shows a dramatic energy-dependence
with relative probability increasing as $\epsilon^{-1/2}$, where $\epsilon$ is
the energy of the system. We simulate low-energy dynamics in both models,
confirming the expected behaviour. We next consider the canonical ensemble,
where the first model produces temperature-independent probabilities. In the
second, relative probability rises sharply as $T^{-1/2}$, where $T$ is the
temperature. Our results bring out a classical analogue of
order-by-singularity, a mechanism that has been recently proposed in the
context of quantum spin clusters. The sampling of classical orders is
qualitatively different in systems with self-intersecting ground state spaces.
It grows at low energies and becomes singular as $\epsilon \rightarrow 0$
(microcanonical ensemble) or $T\rightarrow 0$ (canonical ensemble). We discuss
relevance for disordered phases in macroscopic magnets, particularly for spiral
liquids.
