  We focus on the Gibbs free energy $\Delta G$ for nucleating a droplet of the
stable phase (e.g. solid) inside the metastable parent phase (e.g. liquid),
close to the first-order transition temperature. This quantity is central to
the theory of homogeneous nucleation, since it superintends the nucleation
rate. We recently introduced a field theory describing the dependence of
$\Delta G$ on the droplet volume $V$, taking into account besides the
microscopic fuzziness of the droplet-parent interface, also small fluctuations
around the spherical shape whose effect, assuming isotropy, was found to be a
characteristic logarithmic term. Here we extend this theory, introducing the
effect of anisotropy in the surface tension, and show that in the limit of
strong anisotropy $\Delta G(V)$ once more develops a term logarithmic on $V$,
now with a prefactor of opposite sign with respect to the isotropic case. Based
on this result, we argue that the geometrical shape that large solid nuclei
mostly prefer could be inferred from the prefactor of the logarithmic term in
the droplet free energy, as determined from the optimization of its
near-coexistence profile.

Statistical Mechanics;Mesoscale and Nanoscale Physics;Computational Physics