  Clock-spin models are attracting great interest, due to both their rich phase
diagram and their connection to parafermions. In this context, we derive an
exact local mapping from clock-spin to fermionic partition functions. Such
mapping, akin to techniques introduced by Fedotov and Popov for spin
$\frac{1}{2}$ chains, grants access to well established numerical tools for the
perturbative treatment of fermionic systems in the clock-spin framework.
Moreover, in one dimension, it allows to use bosonization to access the low
energy properties of clock-spin models. Finally, aside from the direct
application in clock-spin models, this new mapping enables the conception of
interesting fermionic models, based on the clock-spin counterparts.
