  Small spin systems at the interface between analytical studies and
experimental application have been intensively studied in recent decades. The
spin ring consisting of four spins with uniform antiferromagnetic Heisenberg
interaction is an example of a completely integrable system, in the double
sense: quantum mechanical and classical. However, this does not automatically
imply that the thermodynamic quantities of the classical system can also be
calculated explicitly. In this work, we derive analytical expressions for the
density of states, the partition function, specific heat, entropy, and
susceptibility. These theoretical results are confirmed by numerical tests.
This allows us to compare the quantum mechanical quantities for increasing spin
quantum numbers $s$ with their classical counterparts in the classical limit
$s\to \infty$. As expected, a good agreement is obtained, except for the low
temperature region. However, this region shrinks with increasing $s$, so that
the classical state variables emerge as envelopes of the quantum mechanical
ones.
