  A few-body cluster is a building block of a many-body system in a gas phase
provided the temperature at most is of the order of the binding energy of this
cluster. Here we illustrate this statement by considering a system of tubes
filled with dipolar distinguishable particles. We calculate the partition
function, which determines the probability to find a few-body cluster at a
given temperature. The input for our calculations -- the energies of few-body
clusters -- is estimated using the harmonic approximation. We first describe
and demonstrate the validity of our numerical procedure. Then we discuss the
results featuring melting of the zero-temperature many-body state into a gas of
free particles and few-body clusters. For temperature higher than its binding
energy threshold, the dimers overwhelmingly dominate the ensemble, where the
remaining probability is in free particles. At very high temperatures free
(harmonic oscillator trap-bound) particle dominance is eventually reached. This
structure evolution appears both for one and two particles in each layer
providing crucial information about the behavior of ultracold dipolar gases.
The investigation addresses the transition region between few and many-body
physics as a function of temperature using a system of ten dipoles in five
tubes.
