Douglas Abraham

Abstract:

Recently an interesting phase transition scenario in the context of a planar Ising system with a grain boundary was revealed [Phys. Rev. Lett. 93, 076101 (2004)]]. In this paper we study in more detail the relaxation dynamics of this system and show how the grain boundary acts as a guide spatially confining matter transport. This is done by performing simulations using the continuous time Monte Carlo algorithm with Kawasaki dynamics. We also set up the problem as a solid-on-solid model and formulate corresponding Langevin equations for the dynamics in two cases, with and without matter conservation.

Abstract:

New exact analytical results are described for surface tension on the triangular Ising lattice. The triangular Ising lattice forms naturally 60degrees and 120degrees corners, and a thermodynamic argument is used, which incorporates the exact results, to obtain conditions for the filling transition for both angles. Monte Carlo simulations with Wang-Landau sampling are performed to independently verify the applicability of this argument. Results are in agreement with previous conjectures for the phase boundary in these systems.