Metastability for the Ising model on the hexagonal lattice

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