  We consider the Ising model on the hexagonal lattice evolving according to
Metropolis dynamics. We study its metastable behavior in the limit of vanishing
temperature when the system is immersed in a small external magnetic field. We
determine the asymptotic properties of the transition time from the metastable
to the stable state up to a multiplicative factor and study the mixing time and
the spectral gap of the Markov process. We give a geometrical description of
the critical configurations and show how not only their size but their shape
varies depending on the thermodynamical parameters. Finally we provide some
results concerning polyiamonds of maximal area and minimal perimeter.
