  We use the free fermionic formulation of the heterotic-string in four
dimensions to study the vacuum structure and energy of non-supersymmetric
tachyon free models that correspond to compactifications of tachyonic vacua of
the ten dimensional heterotic-string. We explore the class of heterotic
$SO(10)$ non-supersymmetric models constructed from the $\tilde{S}$-model in
the Free Fermionic Formalism, and investigate the dependence of the potential
on the geometric moduli. This paper will explore a sample of $ 10^{9}$ string
vacua to find the frequency of viable models, classifying these vacua by the
following fertility criteria: tachyon presence; number of spinorial
$\boldsymbol{16/\overline{16}}$ representations; vectorial $\boldsymbol{10}$
states; Top Quark Mass Coupling compatibility. Of these we find those that
mimic supersymmetric models with equal number of bosons and fermions at the
massless level - $a_{00} = 0$. Tachyon free models occur with a frequency of
$5.309\times10^{-3}$. Furthermore, models that fulfil the rest of the
phenomenological fertility conditions and the additional condition on $a_{00}$
occur with probability $4.0 \times 10^{-9}$ We analyse the partition functions
and study the moduli dependence of such models, finding that almost all fertile
models have finite, positive potential at the Free Fermionic Point, with $2$
out of $84$ of the fertile cores having negative, finite potential. We
demonstratate that the Free Fermionic Point is not necessarily a minimum in the
potential. This work provides further evidence that supersymmetry may not be a
necessary ingredient of phenomenological models, recreating many of the
desirable features of such models without employing supersymmetry.
