In this paper we analyze the metastable behavior for the Ising model thatevolves under Kawasaki dynamics on the hexagonal lattice $\mathbb{H}^2$ in thelimit of vanishing temperature. Let $\Lambda\subset\mathbb{H}^2$ a finite setwhich we assume to be arbitrarily large. Particles perform simple exclusion on$\Lambda$, but when they occupy neighboring sites they feel a binding energy$-U<0$. Along each bond touching the boundary of $\Lambda$ from the outside tothe inside, particles are created with rate $\rho=e^{-\Delta\beta}$, whilealong each bond from the inside to the outside, particles are annihilated withrate 1, where $\beta$ is the inverse temperature and $\Delta>0$ is an activityparameter. For the choice $\Delta\in{(U,\frac{3}{2}U)}$ we prove that the empty(resp.\ full) hexagon is the unique metastable (resp.\ stable) state. Wedetermine the asymptotic properties of the transition time from the metastableto the stable state and we give a description of the critical configurations.We show how not only their size but also their shape varies depending on thethermodynamical parameters. Moreover, we emphasize the role that the specificlattice plays in the analysis of the metastable Kawasaki dynamics by comparingthe different behavior of this system with the corresponding system on thesquare lattice.
Metastability for Kawasaki dynamics on the hexagonal lattice
Simone Baldassarri;
2023-01-01
Abstract
In this paper we analyze the metastable behavior for the Ising model thatevolves under Kawasaki dynamics on the hexagonal lattice $\mathbb{H}^2$ in thelimit of vanishing temperature. Let $\Lambda\subset\mathbb{H}^2$ a finite setwhich we assume to be arbitrarily large. Particles perform simple exclusion on$\Lambda$, but when they occupy neighboring sites they feel a binding energy$-U<0$. Along each bond touching the boundary of $\Lambda$ from the outside tothe inside, particles are created with rate $\rho=e^{-\Delta\beta}$, whilealong each bond from the inside to the outside, particles are annihilated withrate 1, where $\beta$ is the inverse temperature and $\Delta>0$ is an activityparameter. For the choice $\Delta\in{(U,\frac{3}{2}U)}$ we prove that the empty(resp.\ full) hexagon is the unique metastable (resp.\ stable) state. Wedetermine the asymptotic properties of the transition time from the metastableto the stable state and we give a description of the critical configurations.We show how not only their size but also their shape varies depending on thethermodynamical parameters. Moreover, we emphasize the role that the specificlattice plays in the analysis of the metastable Kawasaki dynamics by comparingthe different behavior of this system with the corresponding system on thesquare lattice.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
