Hodge metrics and positivity of direct images

Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This shows that for every holomorphic semi-ample vector bundle $E$ on a complex manifold, and every positive integer $k$, the vector bundle $S^kE\otimes\det E$ has a continuous metric with Griffiths semi-positive curvature. If $E$ is ample on a projective manifold, the metric can be made smooth and Griffiths positive.Comment: revised and expanded version of "A positivity property of ample vector bundles

Cluster derivation of Parisi's RSB solution for disordered systems

We propose a general scheme in which disordered systems are allowed to sacrifice energy equi-partitioning and separate into a hierarchy of ergodic sub-systems (clusters) with different characteristic time-scales and temperatures. The details of the break-up follow from the requirement of stationarity of the entropy of the slower cluster, at every level in the hierarchy. We apply our ideas to the Sherrington-Kirkpatrick model, and show how the Parisi solution can be {\it derived} quantitatively from plausible physical principles. Our approach gives new insight into the physics behind Parisi's solution and its relations with other theories, numerical experiments, and short range models.Comment: 7 pages 5 figure

High pressure high temperature (HPHT) synthesis and magnetization of Magneto-Superconducting RuSr2(LnCe2)Cu2O12.25 (Ru-1232) compounds (Ln = Y and Dy)

RuSr2(LnCe2)Cu2O12.25 (Ru-1232) compounds with Ln = Y and Dy being synthesized by high pressure high temperature (6GPa, 12000C) solid state synthesis route do crystallize in space group P4/mmm in near single phase form with small quantities of SrRuO3 and RuSr2(RE1.5Ce0.5)Cu2O10 (Ru-1222). Both samples exhibit magnetic transitions (Tmag.) at ~90 K with significant branching of zfc (zero-field-cooled) and fc (field-cooled) magnetization and a sharp cusp in zfc at ~ 70 K, followed by superconducting transitions at ~ 30 K. Both compounds show typical ferromagnetic hysteresis loops in magnetic moment (M) versus field (H) magnetization right upto Tmag. i.e. < 90K. To our knowledge these are the first successfully synthesized Ru-1232 compounds in near single phase with lanthanides including Y and Dy. The results are compared with widely reported Gd/Ru-1222 and Ru-1212 (RuSr2GdCu2O8) compounds. In particular, it seems that the Ru moments magnetic ordering temperature (Tmag.) scales with the c-direction distance between magnetic RuO6 octahedras in Ru-1212/1222 or 1232 systems.Comment: 15 pages of TEXT and Fig

Weak Magnetic Order in the Bilayered-hydrate Nax_{x}CoO2⋅y_{2}\cdot yH2_{2}O Structure Probed by Co Nuclear Quadrupole Resonance - Proposed Phase Diagram in Superconducting Nax_xCoO2⋅_{2} \cdot yyH2_2O

A weak magnetic order was found in a non-superconducting bilayered-hydrate Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O sample by a Co Nuclear Quadrupole Resonance (NQR) measurement. The nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ shows a prominent peak at 5.5 K, below which a Co-NQR peak splits due to an internal field at the Co site. From analyses of the Co NQR spectrum at 1.5 K, the internal field is evaluated to be $\sim$ 300 Oe and is in the $ab$-plane. The magnitude of the internal field suggests that the ordered moment is as small as $\sim 0.015$ $\mu_B$ using the hyperfine coupling constant reported previously. It is shown that the NQR frequency $\nu_Q$ correlates with magnetic fluctuations from measurements of NQR spectra and $1/T_1T$ in various samples. The higher-$\nu_Q$ sample has the stronger magnetic fluctuations. A possible phase diagram in Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O is depicted using $T_c$ and $\nu_Q$, in which the crystal distortion along the c-axis of the tilted CoO$_2$ octahedron is considered to be a physical parameter. Superconductivity with the highest $T_c$ is seemingly observed in the vicinity of the magnetic phase, suggesting strongly that the magnetic fluctuations play an important role for the occurrence of the superconductivity.Comment: 5 pages, 6 figures, submitted to J. Phys. Soc. Jp

Anomalous pressure effect on the magnetic ordering in multiferroic BiMnO3

We report the magnetic field dependent dc magnetization and the pressure-dependent (pmax ~ 16 kbar) ac susceptibilities Xp(T) on both powder and bulk multiferroic BiMnO3 samples, synthesized in different batches under high pressure. A clear ferromagnetic (FM) transition is observed at TC ~ 100 K, and increases with magnetic field. The magnetic hysteresis behavior is similar to that of a soft ferromagnet. Ac susceptibility data indicate that both the FM peak and its temperature (TC) decrease simultaneously with increasing pressure. Interestingly, above a certain pressure (9 ~ 11 kbar), another peak appears at Tp ~ 93 K, which also decreases with increasing pressure, with both these peaks persisting over some intermediate pressure range (9 ~ 13 kbar). The FM peak disappears with further application of pressure; however, the second peak survives until present pressure limit (pmax ~ 16 kbar). These features are considered to originate from the complex interplay of the magnetic and orbital structure of BiMnO3 being affected by pressure.Comment: 4 pages,4 figures, publised in Physical Review B 78, 092404/200

Local syzygies of multiplier ideals

In recent years, multiplier ideals have found many applications in local and global algebraic geometry. Because of their importance, there has been some interest in the question of which ideals on a smooth complex variety can be realized as multiplier ideals. Other than integral closure no local obstructions have been known up to now, and in dimension two it was established by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is locally a multiplier ideal. We prove the somewhat unexpected result that multiplier ideals in fact satisfy some rather strong algebraic properties involving higher syzygies. It follows that in dimensions three and higher, multiplier ideals are very special among all integrally closed ideals.Comment: 8 page

Neel Temperature of Quasi-Low-Dimensional Heisenberg Antiferromagnets

The N\'eel temperature, $T_{\rm N}$, of quasi-one- and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of inter-chain (inter-layer) to intra-chain (intra-layer) coupling $J'/J$ down to $J'/J\simeq 10^{-3}$. We find that $T_{\rm N}$ obeys a modified random-phase approximation-like relation for small $J'/J$ with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulae describing $T_{\rm N}$ for a wide range of $J'$ and useful for the analysis of experimental measurements are presented.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Let