  We report some new results on the complex-temperature (CT) singularities of
$q$-state Potts models on the square lattice. We concentrate on the problematic
region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function
are sensitive to finite lattice artifacts. From analyses of low-temperature
series expansions for $3 \le q \le 8$, we establish the existence, in this
region, of complex-conjugate CT singularities at which the magnetization and
susceptibility diverge. From calculations of zeros of the partition function,
we obtain evidence consistent with the inference that these singularities occur
at endpoints $a_e, \ a_e^*$ of arcs protruding into the (complex-temperature
extension of the) FM phase. Exponents for these singularities are determined;
e.g., for $q=3$, we find $\beta_e=-0.125(1)$, consistent with $\beta_e=-1/8$.
By duality, these results also imply associated arcs extending to the (CT
extension of the) symmetric PM phase. Analytic expressions are suggested for
the positions of some of these singularities; e.g., for $q=5$, our finding is
consistent with the exact value $a_e,a_e^*=2(-1 \mp i)$. Further discussions of
complex-temperature phase diagrams are given.
