Non-equilibrium Dynamics of Finite Interfaces

The nanoscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in (electro)chemical potential, are studied by an analytic nonlinear-response approximation together with kinetic Monte Carlo simulations. Here we consider the case that the system is coupled to a two-dimensional phonon bath. In the resu...

It is shown that finite size effects in the free energy of a rough interface of the 3D Ising and three--state Potts models are well described by the capillary wave model at {\em two--loop} order. The agreement between theoretical predictions and Monte Carlo simulations strongly supports the idea of the universality of this description of order--order interfaces in 3D statistical systems above the roughening temperature.

We use a phase-separated driven two-dimensional Ising lattice gas to study fluid interfaces exposed to shear flow parallel to the interface. The interface is stabilized by two parallel walls with opposing surface fields and a driving field parallel to the walls is applied which (i) either acts locally at the walls or (ii) varies linearly with distance across the strip. Using computer simulations with Kawasaki dynamics, we find that the system reaches a steady state in which t...

Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed magnetization when crossing the boundary of the coexistence region. Modifications of this result for systems of spatial dimension greater than two are discussed.

With the Monte Carlo methods, we systematically investigate the short-time dynamics of domain-wall motion in the two-dimensional random-field Ising model with a driving field ?DRFIM?. We accurately determine the depinning transition field and critical exponents. Through two different definitions of the domain interface, we examine the dynamics of overhangs and islands. At the depinning transition, the dynamic effect of overhangs and islands reaches maximum. We argue that this...

We briefly outline the approach to extracting collective dynamics of a domain wall from field equations which has been proposed by us in Nucl.Phys.B450(1995)174-188 and further developed in hep-th/9703168.

The one-dimensional Ising model with nearest neighbour interactions and the zero-temperature dynamics recently considered by Lefevre and Dean -J. Phys. A: Math. Gen. {\bf 34}, L213 (2001)- is investigated. By introducing a particle-hole description, in which the holes are associated to the domain walls of the Ising model, an analytical solution is obtained. The result for the asymptotic energy agrees with that found in the mean field approximation.

We provide accurate Monte Carlo results for the free energy of interfaces with periodic boundary conditions in the 3D Ising model. We study a large range of inverse temperatures, allowing to control corrections to scaling. In addition to square interfaces, we study rectangular interfaces for a large range of aspect ratios u=L_1/L_2. Our numerical results are compared with predictions of effective interface models. This comparison verifies clearly the effective Nambu-Goto mode...

We investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime $|\Delta|< 1$, initially prepared in a product state with two domain walls i.e, $|\downarrow\dots\downarrow\uparrow\dots\uparrow\downarrow\dots\downarrow\rangle$. At early times, the two domain walls evolve independently and only after a calculable time a non-trivial interplay between the two emerges and results in the occurrence of a split Fermi sea. For $\De...

We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties of low energy two-dimensional field theory to determine exact asymptotics of the magnetization profile perperdicularly to the boundary, to show the presence of an interface with endpoints pinned to the boundary, and to determine its passage ...