  The spin-1 classical Blume-Capel model on a square lattice is known to
exhibit a finite-temperature phase transition described by the tricritical
Ising CFT in 1+1 space-time dimensions. This phase transition can be accessed
with classical Monte Carlo simulations, which, via a replica-trick calculation,
can be used to study the shape-dependence of the classical R\'enyi entropies
for a torus divided into two cylinders. From the second R\'enyi entropy, we
calculate the Geometrical Mutual Information (GMI) introduced by St\'ephan et.
al. [Phys. Rev. Lett. 112, 127204 (2014)] and use it to extract a numerical
estimate for the value of the central charge near the tricritical point. By
comparing to the known CFT result, $c=7/10$, we demonstrate how this type of
GMI calculation can be used to estimate the position of the tricritical point
in the phase diagram.
