Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics

C. Godrèche (1) , J.M. Luck (2)

1 SPEC - UMR3680 - Service de physique de l'état condensé
2 SPhT - Service de Physique Théorique

We investigate the motion of a tagged spin in a ferromagnetic Ising chain evolving under Kawasaki dynamics. At equilibrium, the displacement is Gaussian, with a variance growing as $A\,t^{1/2}$. The temperature dependence of the prefactor $A$ is derived exactly. At low temperature, where the static correlation length $\xi$ is large, the mean square displacement grows as $(t/\xi^2)^{2/3}$ in the coarsening regime, i.e., as a finite fraction of the mean square domain length. The case of totally asymmetric dynamics, where $(+)$ (resp.~$(-)$) spins move only to the right (resp.~to the left), is also considered. In the steady state, the displacement variance grows as $B\,t^{2/3}$. The temperature dependence of the prefactor~$B$ is derived exactly, using the Kardar-Parisi-Zhang theory. At low temperature, the displacement variance grows as $t/\xi^2$ in the coarsening regime, again proportionally to the mean square domain length.

Domaines: Physique Générale [physics.gen-ph]; Autre [cond-mat.other]

C. Godrèche, J.M. Luck. Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics. Journal of Physics A: Mathematical and Theoretical, 2003, 36, pp.9973-9989. ⟨hal-00163718⟩