  A practical use of the entanglement entropy in a 1d quantum system is to
identify the conformal field theory describing its critical behavior. It is
exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system,
where $c$ is the central charge of the conformal field theory. Here we define
the geometric mutual information, an analogous quantity for classical critical
points. We compute this for 2d conformal field theories in an arbitrary
geometry, and show in particular that for a rectangle cut into two rectangles,
it is proportional to $c$. This makes it possible to extract $c$ in classical
simulations, which we demonstrate for the critical Ising and 3-state Potts
models.
