On the automorphisms of moduli spaces of curves

In the last years the biregular automorphisms of the Deligne-Mumford's and Hassett's compactifications of the moduli space of n-pointed genus g smooth curves have been extensively studied by A. Bruno and the authors. In this paper we give a survey of these recent results and extend our techniques to some moduli spaces appearing as intermediate steps of the Kapranov's and Keel's realizations of $\bar{M}_{0,n}$, and to the degenerations of Hassett's spaces obtained by allowing zero weights.Comment: 15 pages. The material of version 1 has been reorganized and expanded in this paper and in arXiv:1307.6828 on automorphisms of Hassett's moduli space

Theory of electromagnon in the multiferroic Mn perovskites: Vital role of higher harmonic components of the spiral spin order

We study theoretically the electromagnon and its optical spectrum (OS) of the terahertz-frequency regime in the magnetic-spiral-induced multiferroic phases of the rare-earth (R) Mn perovskites, RMnO3, taking into account the elliptical deformation or the higher harmonics of the spiral spin configuration, which has been missed so far. A realistic spin Hamiltonian, which gives phase diagrams in agreement with experiments, resolves a long standing puzzle, i.e., the double-peak structure of the OS with a larger low-energy peak originating from magnon modes hybridized with the zone-edge state. We also predict the magnon branches associated with the electromagnon, which can be tested by neutron-scattering experiment.Comment: 5 pages, 4 figure

Eternally inflating cosmologies from intersecting spacelike branes

Intersecting spacelike braneworld cosmologies are investigated. The time axis is set on the scale parameter of extra space, which may include more than one timelike metric. Obtained are eternally inflating (i.e. undergoing late-time inflation) Robertson-Walker spacetime and extra space with a constant scale factor. In the case of multibrane solutions, some dimensions are static or shrink. The fact that the largest supersymmetry algebra contains 32 supercharges in 4 dimensions imposes a restriction on the geometry of extra space.Comment: 19 page

Specific Heat and Superfluid Density for Possible Two Different Superconducting States in NaxCoO2.yH2O

Several thermodynamic measurements for the cobaltate superconductor, NaxCoO2.yH2O, have so far provided results inconsistent with each other. In order to solve the discrepancies, we microscopically calculate the temperature dependences of specific heat and superfluid density for this superconductor. We show that two distinct specific-heat data from Oeschler et al. and Jin et al. are reproduced, respectively, for the extended s-wave state and the p-wave state. Two different superfluid-density data are also reproduced for each case. These support our recent proposal of possible two different pairing states in this material. In addition, we discuss the experimentally proposed large residual Sommerfeld coefficient and extremely huge effective carrier mass.Comment: 5 pages, 4 figures, Submitted to J. Phys. Soc. Jp

CoO2-Layer-Thickness Dependence of Magnetic Properties and Possible Two Different Superconducting States in NaxCoO2.yH2O

In order to understand the experimentally proposed phase diagrams of NaxCoO2.yH2O, we theoretically study the CoO2-layer-thickness dependence of magnetic and superconducting (SC) properties by analyzing a multiorbital Hubbard model using the random phase approximation. When the Co valence (s) is +3.4, we show that the magnetic fluctuation exhibits strong layer-thickness dependence where it is enhanced at finite (zero) momentum in the thicker (thinner) layer system. A magnetic order phase appears sandwiched by two SC phases, consistent with the experiments. These two SC phases have different pairing states where one is the singlet extended s-wave state and the other is the triplet p-wave state. On the other hand, only a triplet p-wave SC phase with dome-shaped behavior of Tc is predicted when s=+3.5, which is also consistent with the experiments. Controversial experimental results on the magnetic properties are also discussed.Comment: 5 pages, 4 figures. Submitted to Journal of the Physical Society of Japa

Lattice Distortion and Magnetic Ground State of YTiO3_3 and LaTiO3_3

Effects of lattice distortion on the magnetic ground state of YTiO$_3$ and LaiO$_3$ are investigated on the basis accurate tight-binding parametrization of the $t_{2g}$ electronic structure extracted from the local-density approximation. The complexity of these compounds is related with the fact that the $t_{2g}$-level splitting, caused by lattice distortions, is comparable with the energies of superexchange and spin-orbit interactions. Therefore, all these interactions are equally important and should be treated on an equal footing. The Hartree-Fock approximation fails to provide a coherent description simultaneously for YTiO$_3$ and LaTiO$_3$, and it is essential to go beyond.Comment: 4 pages, 3 figures (good quality figures are available via e-mail

Dynamics of Multiferroic Domain Wall in Spin-Cycloidal Ferroelectric DyMnO3_{3}

We report the dielectric dispersion of the giant magnetocapacitance (GMC) in multiferroic DyMnO$_{3}$ over a wide frequency range. The GMC is found to be attributable not to the softened electromagnon but to the electric-field-driven motion of multiferroic domain wall (DW). In contrast to conventional ferroelectric DWs, the present multiferroic DW motion holds extremely high relaxation rate of $\sim$$10^{7}$ s$^{-1}$ even at low temperatures. This mobile nature as well as the model simulation suggests that the multiferroic DW is not atomically thin as in ferroelectrics but thick, reflecting its magnetic origin.Comment: 4 pages, 4 figure

Microscopic Model and Phase Diagrams of the Multiferroic Perovskite Manganites

Orthorhombically distorted perovskite manganites, RMnO3 with R being a trivalent rare-earth ion, exhibit a variety of magnetic and electric phases including multiferroic (i.e. concurrently magnetic and ferroelectric) phases and fascinating magnetoelectric phenomena. We theoretically study the phase diagram of RMnO3 by constructing a microscopic spin model, which includes not only the superexchange interaction but also the single-ion anisotropy (SIA) and the Dzyaloshinsky-Moriya interaction (DMI). Analysis of this model using the Monte-Carlo method reproduces the experimental phase diagrams as functions of the R-ion radius, which contain two different multiferroic states, i.e. the ab-plane spin cycloid with ferroelectric polarization P//a and the bc-plane spin cycloid with P//c. The orthorhombic lattice distortion or the second-neighbor spin exchanges enhanced by this distortion exquisitely controls the keen competition between these two phases through tuning the SIA and DMI energies. This leads to a lattice-distortion-induced reorientation of P from a to c in agreement with the experiments. We also discuss spin structures in the A-type antiferromagnetic state, those in the cycloidal spin states, origin and nature of the sinusoidal collinear spin state, and many other issues.Comment: 23 pages, 19 figures. Recalculated results after correcting errors in the assignment of Dzyaloshinsky-Moriya vector