On Charge-3 Cyclic Monopoles

We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the theta functions and monopole data of the genus 4 curve to be given in terms of genus 2 data. The Richelot correspondence, a generalization of the arithmetic mean, is used to solve for this genus 2 curve. Results of other approaches are compared.Comment: 34 pages, 16 figures. Revision: Abstract added and a few small change

A semi-small decomposition of the Chow ring of a matroid

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincar\'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations for the Chow ring, recovering the main result of [AHK18]. We also show that a similar semi-small orthogonal decomposition holds for the augmented Chow ring of M

Crystal and magnetic structure of the oxypnictide superconductor LaO(1-x)FxFeAs: evidence for magnetoelastic coupling

High-resolution and high-flux neutron as well as X-ray powder-diffraction experiments were performed on the oxypnictide series LaO(1-x)FxFeAs with 0<x<0.15 in order to study the crystal and magnetic structure. The magnetic symmetry of the undoped compound corresponds to those reported for ReOFeAs (with Re a rare earth) and for AFe2As2 (A=Ba, Sr) materials. We find an ordered magnetic moment of 0.63(1)muB at 2 K in LaOFeAs, which is significantly larger than the values previously reported for this compound. A sizable ordered magnetic moment is observed up to a F-doping of 4.5% whereas there is no magnetic order for a sample with a F concentration of x=0.06. In the undoped sample, several interatomic distances and FeAs4 tetrahedra angles exhibit pronounced anomalies connected with the broad structural transition and with the onset of magnetism supporting the idea of strong magneto-elastic coupling in this material.Comment: 8 pages, 7 figures, regular articl

The oxygen isotope effect in the ab-plane reflectance of underdoped YBa_2Cu_3O_{7-delta}

We have measured the effect of oxygen isotope substitution on the ab-plane reflectance of underdoped YBCO. The frequency shift of the transverse optic phonons due to the substitution of O-16 by O-18 yields an isotope effect of the expected magnitude for copper-oxygen stretching modes with alpha=0.5 +- 0.1. The reflectance shoulder at 400 - 500 cm^-1 shows a much smaller exponent of alpha=0.1 +- 0.1 in the normal state and alpha=0.23+- 0.1 in the superconducting state. These observations suggest that the shoulder is of electronic origin and not due to a phonon mode as has been suggested recently.Comment: 4 pages 2 figure

Renormalization group trajectories from resonance factorized S-matrices

We propose and investigate a large class of models possessing resonance factorized S-matrices. The associated Casimir energy describes a rich pattern of renormalization group trajectories related to flows in the coset models based on the simply laced Lie Algebras. From a simplest resonance S-matrix, satisfying the ``$\phi^3$-property'', we predict new flows in non-unitary minimal models.Comment: (7 pages) (no figures included

High resolution X-ray scattering studies of structural phase transitions in underdoped La2−x_{2-x}Bax_xCuO4_4

We have studied structural phase transitions in high quality underdoped La$_{2-x}$Ba$_x$CuO$_4$ single crystals using high resolution x-ray scattering techniques. Critical properties associated with the continuous High Temperature Tetragonal (HTT, $I4/mmm$) to Middle Temperature Orthorhombic (MTO, $Cmca$) phase transition were investigated in single crystal samples with x=0.125, 0.095, and 0.08 and we find that all behavior is consistent with three dimensional XY criticality, as expected from theory. Power law behavior in the orthorhombic strain, 2(a-b)/(a+b), is observed over a remarkably wide temperature range, spanning most of the MTO regime in the phase diagram. Low temperature measurements investigating the Low Temperature Tetragonal (LTT, $P4_{2}/ncm$) phase, below the strongly discontinuous MTO$\to$LTT phase transition, in x=0.125 and x=0.095 samples show that the LTT phase is characterized by relatively broad Bragg scattering, compared with that observed at related wavevectors in the HTT phase. This shows that the LTT phase is either an admixture of tetragonal and orthorhombic phases, or that it is orthorhombic with very small orthorhombic strain, consistent with the ``less orthorhombic" low temperature structure previously reported in mixed La$_{2-x}$Sr$_{x-y}$Ba$_y$CuO$_4$ single crystals. We compare the complex temperature-composition phase diagram for the location of structural and superconducting phase transitions in underdoped La$_{2-x}$Ba$_x$CuO$_4$ and find good agreement with results obtained on polycrystalline samples.Comment: 8 pages, 7 figures, 1 tabl

Evidence for incommensurate spin fluctuations in Sr_2RuO_4

We report first inelastic neutron scattering measurements in the normal state of Sr_2RuO_4 that reveal the existence of incommensurate magnetic spin fluctuations located at ${\bf q}_0=(\pm 0.6\pi/a, \pm 0.6\pi/a, 0)$. This finding confirms recent band structure calculations that have predicted incommensurate magnetic responses related to dynamical nesting properties of its Fermi surface