Non-equilibrium Dynamics of Finite Interfaces

This paper gives a pedagogical introduction to the mechanics of ferromagnetic solitons. We start with the dynamics of a single spin and develop all the tools required for the description of the dynamics of solitons in a ferromagnet.

Using theories of phase ordering kinetics and of renormalization group, we derive analytically the relaxation times of the long wave-length fluctuations of a phase-separated domain boundary in the vicinity of (and below) the critical temperature, in the planar Ising universality class. For a conserved order parameter, the relaxation time grows like $\Lambda^3$ at wave-length $\Lambda$ and can be expressed in terms of parameters relevant at the microscopic scale: lattice spaci...

The interface between domains of opposite magnetization in the 3D Ising model near the critical temperature displays universal finite-size effects which can be described in terms of a gaussian model of capillary waves. It turns out that these finite-size corrections depend rather strongly on the shape of the lattice. This prediction, which has no adjustable parameters, is tested and accurately verified for various lattice shapes by means of numerical simulations with a cluste...

We investigate analytically and numerically the dynamics of domain walls in a spin chain with ferromagnetic Ising interaction and subject to an external magnetic field perpendicular to the easy magnetization axis (transverse field Ising model). The analytical results obtained within the continuum approximation and numerical simulations performed for discrete classical model are used to analyze the quantum properties of domain walls using the semiclassical approximation. We sh...

We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field theories are used in order to find exact analytic results for one- and two-point correlation functions of both the energy density and order parameter fields. The subleading finite-size corrections are also computed and interpreted ...

Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.

We compute thermal and quantum fluctuations in the background of a domain wall in a scalar field theory at finite temperature using the exact scalar propagator in the subspace orthogonal to the wall's translational mode. The propagator makes it possible to calculate terms of any order in the semiclassical expansion of the partition function of the system. The leading term in the expansion corresponds to the fluctuation determinant, which we compute for arbitrary temperature i...

We present exact derivations of the effective capillary wave fluctuation induced forces resulting from pinning of an interface between two coexisting phases at two points separated by a distance r. In two dimensions the Ising ferromagnet calculations based on the transfer matrix approach give an attractive force decaying as 1/r for large distances. In three dimensions mapping of the body-centered solid-on-solid model onto the 6-vertex model allows for exact solution using the...

We investigate how the scaling behavior of finite systems at magnetic first-order transitions (FOTs) with relaxational dynamics changes in correspondence of various boundary conditions. As a theoretical laboratory we consider the two-dimensional Ising model in the low-temperature phase. When the boundary conditions do not favor any specific phase of the system, we show that a dynamic finite-size scaling (DFSS) theory can be developed to describe the dynamic behavior in the co...

Interface localization-delocalization transitions (ILDT) occur in two-phase fluids confined in a slit with competing preferences of the walls for the two fluid phases. At low temperatures the interface between the two phases is localized at one of the walls. Upon increasing temperature it unbinds. Although intensively studied theoretically and computationally, such transitions have not yet been observed experimentally due to severe challenges in resolving fine details of the ...