Generalized nonlinear sigma model approach to alternating spin chains and ladders

We generalize the nonlinear sigma model treatment of quantum spin chains to cases including ferromagnetic bonds. When these bonds are strong enough, the classical ground state is no longer the standard Neel order and we present an extension of the known formalism to deal with this situation. We study the alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The smooth crossover between decoupled dimers and the Haldane phase is semi-quantitatively reproduced. We study also a spin ladder with diagonal exchange couplings that interpolates between the gapped phase of the two-leg spin ladder and the Haldane phase. Here again we show that there is good agreement between DMRG data and our analytical results.Comment: 10 pages, 5 encapsulated figures, REVTeX 3.

Tasting edge effects

We show that the baking of potato wedges constitutes a crunchy example of edge effects, which are usually demonstrated in electrostatics. A simple model of the diffusive transport of water vapor around the potato wedges shows that the water vapor flux diverges at the sharp edges in analogy with its electrostatic counterpart. This increased evaporation at the edges leads to the crispy taste of these parts of the potatoes.Comment: to appear in American Journal of Physic

Estimating model evidence using data assimilation

We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the discrimination between a factual model–which corresponds, to the best of the modeller's knowledge, to the situation in the actual world in which a sequence of events has occurred–and a counterfactual model, in which a particular forcing or process might be absent or just quantitatively different from the actual world. Three different ensemble‐DA methods are reviewed for this purpose: the ensemble Kalman filter (EnKF), the ensemble four‐dimensional variational smoother (En‐4D‐Var), and the iterative ensemble Kalman smoother (IEnKS). An original contextual formulation of model evidence (CME) is introduced. It is shown how to apply these three methods to compute CME, using the approximated time‐dependent probability distribution functions (pdfs) each of them provide in the process of state estimation. The theoretical formulae so derived are applied to two simplified nonlinear and chaotic models: (i) the Lorenz three‐variable convection model (L63), and (ii) the Lorenz 40‐variable midlatitude atmospheric dynamics model (L95). The numerical results of these three DA‐based methods and those of an integration based on importance sampling are compared. It is found that better CME estimates are obtained by using DA, and the IEnKS method appears to be best among the DA methods. Differences among the performance of the three DA‐based methods are discussed as a function of model properties. Finally, the methodology is implemented for parameter estimation and for event attribution

Effective interactions and phase behaviour for a model clay suspension in an electrolyte

Since the early observation of nematic phases of disc-like clay colloids by Langmuir in 1938, the phase behaviour of such systems has resisted theoretical understanding. The main reason is that there is no satisfactory generalization for charged discs of the isotropic DLVO potential describing the effective interactions between a pair of spherical colloids in an electrolyte. In this contribution, we show how to construct such a pair potential, incorporating approximately both the non-linear effects of counter-ion condensation (charge renormalization) and the anisotropy of the charged platelets. The consequences on the phase behaviour of Laponite dispersions (thin discs of 30 nm diameter and 1 nm thickness) are discussed, and investigation into the mesostructure via Monte Carlo simulations are presented.Comment: LaTeX, 12 pages, 11 figure

Nuclear Matter in Intense Magnetic Field and Weak Processes

We study the effect of magnetic field on the dominant neutrino emission processes in neutron stars.The processes are first calculated for the case when the magnetic field does not exceed the critical value to confine electrons to the lowest Landau state.We then consider the more important case of intense magnetic field to evaluate the direct URCA and the neutronisation processes. In order to estimate the effect we derive the composition of cold nuclear matter at high densities and in beta equilibrium, a situation appropriate for neutron stars. The hadronic interactions are incorporated through the exchange of scalar and vector mesons in the frame work of relativistic mean field theory. In addition the effects of anomalous magnetic moments of nucleons are also considered.Comment: 29 pages (LaTeX) including 7 figure

Searching for activated transitions in complex magnetic systems

The process of finding activated transitions in localized spin systems with continuous degrees of freedom is developed based on a magnetic variant of the Activation-Relaxation Technique (mART). In addition to the description of the method and the relevant local properties of the magnetic energy landscape, a criterion to efficiently recognize failed attempts and an expression for the step magnitude to control the convergence are proposed irrespective of the physical system under study. The present implementation is validated on two translational symmetric systems with isotropic exchange interactions. Then, in one example, diffusion processes of a skyrmion vacancy and a skyrmion interstitial are revealed for a skyrmion system on a square spin lattice. In another example, the set of activation events about a metastable state of a 2D dipolar spin glass is investigated and the corresponding energy barrier distribution is found. Detailed inspection of the transition states reveals the participation of nearest neighbour pairs affording a simplified analytical understanding