We compute the vacuum polarization energy of kink solitons in the $phi^{8}$ model in one space and one time dimensions. There are three possible field potentials that have eight powers of $phi$ and that possess kink solitons. For these different field potentials we investigate whether the vacuum polarization destabilizes thesolitons. This may particularly be the case for those potentials that have degenerate ground states with different curvatures in field space yielding different thresholds for the quantum fluctuations about the solitons at negative and positive spatial infinity. We find that destabilization occurs in some cases, but this is not purely a matter of the field potential but also depends on the realized soliton solution for that potential. One of the possible field potentials has solitons with different topological charges. In that case the classical mass approximately scales like the topological charge. Even though destabilization precludes robust statements, there are indications that the vacuum polarization energy does not scale as the topological charge.
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