2 research outputs found
Metastability for the Ising model on the hexagonal lattice
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 and study the relaxation 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