Dipolar ground state of planar spins on triangular lattices

An infinite triangular lattice of classical dipolar spins is usually considered to have a ferromagnetic ground state. We examine the validity of this statement for finite lattices and in the limit of large lattices. We find that the ground state of rectangular arrays is strongly dependent on size and aspect ratio. Three results emerge that are significant for understanding the ground state properties: i) formation of domain walls is energetically favored for aspect ratios below a critical valu e; ii) the vortex state is always energetically favored in the thermodynamic limit of an infinite number of spins, but nevertheless such a configuration may not be observed even in very large lattices if the aspect ratio is large; iii) finite range approximations to actual dipole sums may not provide the correct ground sta te configuration because the ferromagnetic state is linearly unstable and the domain wall energy is negative for any finite range cutoff.Comment: Several short parts have been rewritten. Accepted for publication as a Rapid Communication in Phys. Rev.

Market microstructure, bank's behaviour and interbank spreads

We present an empirical analysis of the European electronic interbank market of overnight lending (e-MID) during the years 1999–2009. The main goal of the paper is to explain the observed changes of the cross-sectional dispersion of lending/borrowing conditions before, during and after the 2007–2008 subprime crisis. Unlike previous contributions, that focused on banks’ dependent and macro information as explanatory variables, we address the role of banks’ behaviour and market microstructure as determinants of the credit spreads

Dynamic binding of driven interfaces in coupled ultrathin ferromagnetic layers

We demonstrate experimentally dynamic interface binding in a system consisting of two coupled ferromagnetic layers. While domain walls in each layer have different velocity-field responses, for two broad ranges of the driving field, H, walls in the two layers are bound and move at a common velocity. The bound states have their own velocity-field response and arise when the isolated wall velocities in each layer are close, a condition which always occurs as H->0. Several features of the bound states are reproduced using a one dimensional model, illustrating their general nature.Comment: 5 pages, 4 figures, to be published in Physical Review Letter

Nonmonotonic roughness evolution in unstable growth

The roughness of vapor-deposited thin films can display a nonmonotonic dependence on film thickness, if the smoothening of the small-scale features of the substrate dominates over growth-induced roughening in the early stage of evolution. We present a detailed analysis of this phenomenon in the framework of the continuum theory of unstable homoepitaxy. Using the spherical approximation of phase ordering kinetics, the effect of nonlinearities and noise can be treated explicitly. The substrate roughness is characterized by the dimensionless parameter $Q = W_0/(k_0 a^2)$, where $W_0$ denotes the roughness amplitude, $k_0$ is the small scale cutoff wavenumber of the roughness spectrum, and $a$ is the lattice constant. Depending on $Q$, the diffusion length $l_D$ and the Ehrlich-Schwoebel length $l_{ES}$, five regimes are identified in which the position of the roughness minimum is determined by different physical mechanisms. The analytic estimates are compared by numerical simulations of the full nonlinear evolution equation.Comment: 16 pages, 6 figures, to appear on Phys. Rev.

Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model

We investigate the geometrical structure of instabilities in the two-scale Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle in tangent space, composed by a set of vectors with a significant projection onto the slow degrees of freedom; they correspond to the smallest (in absolute value) Lyapunov exponents and thereby to the longer timescales. We show that the dimension of the slow bundle is extensive in the number of both slow and fast degrees of freedom and discuss its relationship with the results of a finite-size analysis of instabilities, supporting the conjecture that the slow-variable behavior is effectively determined by a nontrivial subset of degrees of freedom. More precisely, we show that the slow bundle corresponds to the Lyapunov spectrum region where fast and slow instability rates overlap, “mixing” their evolution into a set of vectors which simultaneously carry information on both scales. We suggest that these results may pave the way for future applications to ensemble forecasting and data assimilations in weather and climate models

Low-Temperature Quantum Relaxation in a System of Magnetic Nanomolecules

We argue that to explain recent resonant tunneling experiments on crystals of Mn$_{12}$ and Fe$_8$, particularly in the low-T limit, one must invoke dynamic nuclear spin and dipolar interactions. We show the low-$T$, short-time relaxation will then have a $\sqrt{t/\tau}$ form, where $\tau$ depends on the nuclear $T_2$, on the tunneling matrix element $\Delta_{10}$ between the two lowest levels, and on the initial distribution of internal fields in the sample, which depends very strongly on sample shape. The results are directly applicable to the $Fe_8$ system. We also give some results for the long-time relaxation.Comment: 4 pages, 3 PostScript figures, LaTe

A large-deviation approach to space-time chaos

In this Letter we show that the analysis of Lyapunov-exponents fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a Gaussian approximation for the large deviation function that quantifies the fluctuation probability. More precisely, a diffusion matrix $\bf D$ (a dynamical invariant itself) is measured and analysed in terms of its principal components. The application of this method to three (conservative, as well as dissipative) models, allows: (i) quantifying the strength of the effective interactions among the different degrees of freedom; (ii) unveiling microscopic constraints such as those associated to a symplectic structure; (iii) checking the hyperbolicity of the dynamics.Comment: 4 pages, 3 figures. To appear in Phys. Rev. Let

From multiplicative noise to directed percolation in wetting transitions

A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behaviour observed along the transition line changes from a directed-percolation to a multiplicative-noise type. Numerical simulations allow for a quantitative study of the multicritical point separating the two regions, Mean-field arguments and the mapping on a yet simpler model provide some further insight on the overall scenario.Comment: 4 pages, 3 figure

Absence of stable collinear configurations in Ni(001)ultrathin films: canted domain structure as ground state

Brillouin light scattering (BLS) measurements were performed for (17-120) Angstrom thick Cu/Ni/Cu/Si(001) films. A monotonic dependence of the frequency of the uniform mode on an in-plane magnetic field H was observed both on increasing and on decreasing H in the range (2-14) kOe, suggesting the absence of a metastable collinear perpendicular ground state. Further investigation by magneto-optical vector magnetometry (MOKE-VM) in an unconventional canted-field geometry provided evidence for a domain structure where the magnetization is canted with respect to the perpendicular to the film. Spin wave calculations confirm the absence of stable collinear configurations.Comment: 6 pages, 3 figures (text, appendix and 1 figure added

On the relationship between directed percolation and the synchronization transition in spatially extended systems

We study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model. An analytic argument is put forward showing that, in the limit of discontinuous processes, the transition belongs to the directed percolation (DP) universality class. The analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold. We find the existence of a critical threshold separating the regime controlled by linear mechanisms from that controlled by collective phenomena. As a result of this analysis we conclude that the synchronization transition belongs to the DP class also in continuous models. The conclusions are supported by numerical checks on coupled map lattices too