The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs

We study with Monte Carlo methods an ensemble of c=-5 gravity graphs, generated by coupling a conformal field theory with central charge c=-5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent gamma_s and the intrinsic fractal dimensions d_H. We find gamma_s = -1.5(1) and d_H = 3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, provided the total central charge of the matter sector is c=-5. From this we conjecture that the critical behavior of the Ising model is determined solely by the average fractal properties of the graphs, the coupling to the geometry not playing an important role.Comment: 23 pages, Latex, 7 figure

The Flat Phase of Crystalline Membranes

We present the results of a high-statistics Monte Carlo simulation of a phantom crystalline (fixed-connectivity) membrane with free boundary. We verify the existence of a flat phase by examining lattices of size up to $128^2$. The Hamiltonian of the model is the sum of a simple spring pair potential, with no hard-core repulsion, and bending energy. The only free parameter is the the bending rigidity $\kappa$. In-plane elastic constants are not explicitly introduced. We obtain the remarkable result that this simple model dynamically generates the elastic constants required to stabilise the flat phase. We present measurements of the size (Flory) exponent $\nu$ and the roughness exponent $\zeta$. We also determine the critical exponents $\eta$ and $\eta_u$ describing the scale dependence of the bending rigidity ($\kappa(q) \sim q^{-\eta}$) and the induced elastic constants ($\lambda(q) \sim \mu(q) \sim q^{\eta_u}$). At bending rigidity $\kappa = 1.1$, we find $\nu = 0.95(5)$ (Hausdorff dimension $d_H = 2/\nu = 2.1(1)$), $\zeta = 0.64(2)$ and $\eta_u = 0.50(1)$. These results are consistent with the scaling relation $\zeta = (2+\eta_u)/4$. The additional scaling relation $\eta = 2(1-\zeta)$ implies $\eta = 0.72(4)$. A direct measurement of $\eta$ from the power-law decay of the normal-normal correlation function yields $\eta \approx 0.6$ on the $128^2$ lattice.Comment: Latex, 31 Pages with 14 figures. Improved introduction, appendix A and discussion of numerical methods. Some references added. Revised version to appear in J. Phys.

Characteristics of <u>></u> 290 keV magnetosheath ions

International audienceWe performed a statistical analysis of 290-500 keV ion data obtained by IMP-8 during the years 1982-1988 within the earth's magnetosheath and analysed in detail some time periods withdistinct ion bursts. These studies reveal the following characteristics for magnetosheath 290-500 keV energetic ions: (a) the occurrence frequency and the flux of ions increase with increasing geomagnetic activity as indicated by the Kp index; the occurrence frequency was found to be as high as P > 42% for Kp > 2, (b) the occurrence frequency in the dusk magnetosheath was found to be slightly dependent on the local time and ranged between ~30% and ~46% for all Kp values; the highest occurrence frequency was detected near the dusk magnetopause (21 LT), (c) the high energy ion bursts display a dawn-dusk asymmetry in their maximum fluxes, with higher fluxes appearing in the dusk magnetosheath, and (d) the observations in the dusk magnetosheath suggest that there exist intensity gradients of energetic ions from the bow shock toward the magnetopause. The statistical results are consistent with the concept that leakage of magnetospheric ions from the dusk magnetopause is a semi-permanent physical process often providing the magnetosheath with high energy (290-500 keV) ions

Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for 0<c<10 < c < 1

We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and three--states Potts model matter. By measuring spin-spin correlation functions as a function of the geodesic distance we provide substantial evidence for a diverging correlation length at $\beta_c$. The corresponding scaling exponents are directly related to the KPZ exponents of the matter fields as conjectured in [4] (NPB454(1995)313).Comment: Talk presented at LATTICE96(gravity

Energy time dispersion of a new class of magnetospheric ion events observed near the Earth's bow shock

International audienceWe have analyzed high time resolution (\geq6 s) data during the onset and the decay phase of several energetic (\geq35 keV) ion events observed near the Earth's bow shock by the CCE/AMPTE and IMP-7/8 spacecraft, during times of intense substorm/geomagnetic activity. We found that forward energy dispersion at the onset of events (earlier increase of middle energy ions) and/or a delayed fall of the middle energy ion fluxes at the end of events are often evident in high time resolution data. The energy spectra at the onset and the decay of this kind of events show a characteristic hump at middle (50-120 keV) energies and the angular distributions display either anisotropic or broad forms. The time scale of energy dispersion in the ion events examined was found to range from several seconds to \sim1 h depending on the ion energies compared and on the rate of variation of the Interplanetary Magnetic Field (IMF) direction. Several canditate processes are discussed to explain the observations and it is suggested that a rigidity dependent transport process of magnetospheric particles within the magnetosheath is most probably responsible for the detection of this new type of near bow shock magnetospheric ion events. The new class of ion events was observed within both the magnetosheath and the upstream region

Bridging the university-school divide - Horizontal expertise and the two-worlds pitfall

Research on teacher learning consistently documents the disjuncture between the practices beginning teachers encounter in university teacher preparation courses and those they reencounter in the K-12 classrooms in which they learn to teach. As preservice teachers enter teaching, they gravitate toward conventional K-12 practices, dismissing those endorsed by the university as impractical. In this article, the authors delineate the concept of horizontal expertise and document how its production and use can address this “two-worlds pitfall.” Drawing on the authors\u27 work creating a cross-institutional collaborative, they identify three processes central to the production of horizontal expertise in teacher education: the exchange of tools, the negotiation of social languages, and argumentation. They then trace its use across the university and school settings to show how horizontal expertise can rescript mentoring and expand dialogic practices in the university. The authors conclude by identifying the challenges of developing horizontal expertise in teacher educatio