We extend the classification of fermionic $\mathbb{Z}_2\times\mathbb{Z}_2$ heterotic string orbifolds to non--supersymmetric Pati--Salam (PS) models in two classes vacua, that we dub $\tilde S$--models and $S$--models. The first correspond compactifications a tachyonic ten--dimensional vacuum, whereas second tachyon--free $SO(16)\times SO(16)$ string. In both cases develop systematic method ext...

Z-strings in the Weinberg-Salam model including fermions are unstable for all values of the parameters. The cause of this instability is the fermion vacuum energy in the Z-string background. Z-strings with non-zero fermion densities, however, may still be stable. ⋆ e-mail: [email protected] The recent discovery of cosmic string solutions in the Weinberg-Salam model of electroweak inter...