Complexes of stationary domain walls in the resonantly forced Ginsburg-Landau equation

The parametrically driven Ginsburg-Landau equation has well-known stationary solutions -- the so-called Bloch and Neel, or Ising, walls. In this paper, we construct an explicit stationary solution describing a bound state of two walls. We also demonstrate that stationary complexes of more than two walls do not exist.Comment: 10 pages, 2 figures, to appear in Physical Review

Dipolar Ordering and Quantum Dynamics of Domain Walls in Mn-12 Acetate

We find that dipolar interactions favor ferromagnetic ordering of elongated crystals of Mn12 Acetate below 0.8 K. Ordered crystals must possess domain walls. Motion of the wall corresponds to a moving front of Landau-Zener transitions between quantum spin levels. Structure and mobility of the wall are computed. The effect is robust with respect to inhomogeneous broadening and decoherence.Comment: 11 PR pages, 4 figures. This is the extended versio

Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatio-temporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.Comment: Text: 14 pages compressed Postscript (90kb) Figures: 9 pages compressed Postscript (368kb

Roughening Transition of Interfaces in Disordered Systems

The behavior of interfaces in the presence of both lattice pinning and random field (RF) or random bond (RB) disorder is studied using scaling arguments and functional renormalization techniques. For the first time we show that there is a continuous disorder driven roughening transition from a flat to a rough state for internal interface dimensions 2<D<4. The critical exponents are calculated in an \epsilon-expansion. At the transition the interface shows a superuniversal logarithmic roughness for both RF and RB systems. A transition does not exist at the upper critical dimension D_c=4. The transition is expected to be observable in systems with dipolar interactions by tuning the temperature.Comment: 4 pages, RevTeX, 1 postscript figur

Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns

Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a variational principle far from equilibrium allows the coexistence of domain walls propagating in any direction. As a consequence, *persistent* patterns may emerge. We study this mechanism of pattern formation using a non-variational extension of Landau's model for second order phase transitions. PACS numbers: 05.70.Fh, 42.65.Pc, 47.20.Ky, 82.20MjComment: 12 pages LaTeX, 5 postscript figures To appear in Phys. Rev.

Points, Walls and Loops in Resonant Oscillatory Media

In an experiment of oscillatory media, domains and walls are formed under the parametric resonance with a frequency double the natural one. In this bi-stable system, %phase jumps $\pi$ by crossing walls. a nonequilibrium transition from Ising wall to Bloch wall consistent with prediction is confirmed experimentally. The Bloch wall moves in the direction determined by its chirality with a constant speed. As a new type of moving structure in two-dimension, a traveling loop consisting of two walls and Neel points is observed.Comment: 9 pages (revtex format) and 6 figures (PostScript

Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations

We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is therefore realized either along one trajectory or along two equivalent paths. Zero point fluctuations smear out the sharp transition between these two regimes and lead to a certain crossover behavior. When the two saddle points are inequivalent one can also have a first order transition related to the fact that one of the two trajectories becomes unstable. We illustrate these results by numerical investigations. Even though a specific model is investigated here, the approach is quite general and has potential applicability for various systems in physics and chemistry exhibiting multi-stability and tunneling phenomena.Comment: 11 pages, 8 eps figures, Revtex-

Bloch-Wall Phase Transition in the Spherical Model

The temperature-induced second-order phase transition from Bloch to linear (Ising-like) domain walls in uniaxial ferromagnets is investigated for the model of D-component classical spin vectors in the limit D \to \infty. This exactly soluble model is equivalent to the standard spherical model in the homogeneous case, but deviates from it and is free from unphysical behavior in a general inhomogeneous situation. It is shown that the thermal fluctuations of the transverse magnetization in the wall (the Bloch-wall order parameter) result in the diminishing of the wall transition temperature T_B in comparison to its mean-field value, thus favouring the existence of linear walls. For finite values of T_B an additional anisotropy in the basis plane x,y is required; in purely uniaxial ferromagnets a domain wall behaves like a 2-dimensional system with a continuous spin symmetry and does not order into the Bloch one.Comment: 16 pages, 2 figure

Domain wall roughening in dipolar films in the presence of disorder

We derive a low-energy Hamiltonian for the elastic energy of a N\'eel domain wall in a thin film with in-plane magnetization, where we consider the contribution of the long-range dipolar interaction beyond the quadratic approximation. We show that such a Hamiltonian is analogous to the Hamiltonian of a one-dimensional polaron in an external random potential. We use a replica variational method to compute the roughening exponent of the domain wall for the case of two-dimensional dipolar interactions.Comment: REVTEX, 35 pages, 2 figures. The text suffered minor changes and references 1,2 and 12 were added to conform with the referee's repor