  In various statistical-mechanical models the introduction of a metric onto
the space of parameters (e.g. the temperature variable, $\beta$, and the
external field variable, $h$, in the case of spin models) gives an alternative
perspective on the phase structure. For the one-dimensional Ising model the
scalar curvature, ${\cal R}$, of this metric can be calculated explicitly in
the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) /
\sqrt{\sinh^2 (h) + \exp (- 4 \beta)}$. This is positive definite and, for
physical fields and temperatures, diverges only at the zero-temperature,
zero-field ``critical point'' of the model.
  In this note we calculate ${\cal R}$ for the one-dimensional $q$-state Potts
model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B
(q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts
analogue of $\sinh^2 (h) + \exp (- 4 \beta)$. This is no longer positive
definite, but once again it diverges only at the critical point in the space of
real parameters. We remark, however, that a naive analytic continuation to
complex field reveals a further divergence in the Ising and Potts curvatures at
the Lee-Yang edge.
