Zero Temperature Phase Transition in Spin-ladders: Phase Diagram and Dynamical studies of Cu(Hp)Cl

In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields Hc1 and Hc2. An experimental review of static and dynamical properties of spin-ladders close to these critical points is presented. The scaling functions, universal to all quantum critical points in one-dimension, are extracted from (a) the thermodynamic quantities (magnetization) and (b) the dynamical functions (NMR relaxation). A simple mapping of strongly coupled spin ladders in a magnetic field on the exactly solvable XXZ model enables to make detailed fits and gives an overall understanding of a broad class of quantum magnets in their gapless phase (between Hc1 and Hc2). In this phase, the low temperature divergence of the NMR relaxation demonstrates its Luttinger liquid nature as well as the novel quantum critical regime at higher temperature. The general behaviour close these quantum critical points can be tied to known models of quantum magnetism.Comment: few corrections made, 15 pages, to be published in European Journal of Physics

Magnetoresistance due to Domain Walls in Micron Scale Fe Wires with Stripe Domains

The magnetoresistance (MR) associated with domain boundaries has been investigated in microfabricated bcc Fe (0.65 to 20 $\mu$m linewidth) wires with controlled stripe domains. Domain configurations have been characterized using magnetic force microscopy. MR measurements as a function of field angle, temperature and domain configuration are used to estimate MR contributions due to resistivity anisotropy and domain walls. Evidence is presented that domain boundaries enhance the conductivity in such microstructures over a broad range of temperatures (1.5 K to 80 K).Comment: 8 pages, 3 postscript figures, and 2 jpg images (Fig 1 and 2) to appear in IEEE Transactions on Magnetics (Fall 1998

Luttinger liquid behavior in weakly disordered quantum wires

We have measured the temperature dependence of the conductance in long V-groove quantum wires (QWRs) fabricated in GaAs/AlGaAs heterostructures. Our data is consistent with recent theories developed within the framework of the Luttinger liquid model, in the limit of weakly disordered wires. We show that for the relatively small amount of disorder in our QWRs, the value of the interaction parameter g is g=0.66, which is the expected value for GaAs. However, samples with a higher level of disorder show conductance with stronger temperature dependence, which does not allow their treatment in the framework of perturbation theory. Trying to fit such data with perturbation-theory models leads inevitably to wrong (lower) values of g.Comment: 4 pages, 4 figure

Learning cover context-free grammars from structural data

We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most $\ell.$ The goal is to learn a cover context-free grammar (CCFG) with respect to $\ell$, that is, a CFG whose structural descriptions with depth at most $\ell$ agree with those of the unknown CFG. We propose an algorithm, called $LA^\ell$, that efficiently learns a CCFG using two types of queries: structural equivalence and structural membership. We show that $LA^\ell$ runs in time polynomial in the number of states of a minimal deterministic finite cover tree automaton (DCTA) with respect to $\ell$. This number is often much smaller than the number of states of a minimum deterministic finite tree automaton for the structural descriptions of the unknown grammar

Comment on: Role of Intermittency in Urban Development: A Model of Large-Scale City Formation

Comment to D.H. Zanette and S.C. Manrubia, Phys. Rev. Lett. 79, 523 (1997).Comment: 1 page no figure