A connection between the Ice-type model of Linus Pauling and the three-color problem

The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e.,colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of $N$ oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case $N\rightarrow \infty$ which is compared with the exact solution by Lieb.Comment: 25 pages, 10 figure

A search for the fourth SM family quarks at Tevatron

It is shown that the fourth standard model (SM) family quarks can be observed at the Fermilab Tevatron if their anomalous interactions with known quarks have sufficient strength.Comment: 7 pages, 2 tables, 4 figure

Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB6_6

A minimal model for multipole orders in CeB$_6$ shows that degeneracy of the quadrupole order parameters and strong spin-orbit coupling lead to peculiar temperature and magnetic-field dependences of the X-ray reflection intensity at superlattice Bragg points. Furthermore, the intensity depends sensitively on the surface direction. These theoretical results explain naturally recent X-ray experiments in phases II and III of CeB$_6$. It is predicted that under weak magnetic field perpendicular to the (111) surface, the reflection intensity should change non-monotonically as a function of temperature.Comment: 4 pages, 5 figure

Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise

A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong.Comment: 11 pages, 6 figures, other comment

Resonant X-Ray Scattering from the Quadrupolar Ordering Phase of CeB_6

We theoretically investigate the origin of the resonant x-ray scattering (RXS) signal near the Ce $L_{III}$ absorption edge in the quadrupolar ordering phase of CeB$_6$, considering the intersite interaction between the $\Gamma_8$ states in the initial state. The anisotropic charge distribution of the $4f$ states modulates the $5d$ states through the intra-atomic Coulomb interaction and thereby generates a large RXS superlattice intensity. The temperature and magnetic field dependence indicates that the induced dipolar and octupolar orders have little influence on the RXS spectra, in good agreement with the recent experiment.Comment: 4 pages, 4 figure

The structure of the extreme Schwarzschild-de Sitter space-time

The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global structure of this space-time is here analyzed in detail. Conformal and embedding diagrams are constructed, and synchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture are presented. The permitted geodesic motions are also analyzed. By a careful investigation of the geodesics and the equations of geodesic deviation, it is shown that specific families of observers escape from falling into the singularity and approach nonsingular asymptotic regions which are represented by special "points" in the complete conformal diagram. The redshift of signals emitted by particles which fall into the singularity, as detected by those observers which escape, is also calculated.Comment: 19 pages, 10 figures, LaTeX, to appear in Gen. Rel. Gra

Lattice Distortion and Resonant X-Ray Scattering in DyB2C2

We study the resonant x-ray scattering (RXS) spectra at the Dy $L_{\rm III}$ absorption edge in the quadrupole ordering phase of DyB$_2$C$_2$. Analyzing the buckling of sheets of B and C atoms, we construct an effective model that the crystal field is acting on the $5d$ and $4f$ states with the principal axes different for different sublattices. Treating the $5d$ states as a band and the $4f$ states as localized states, we calculate the spectra within the dipole transition. We take account of processes that (1) the lattice distortion directly modulates the $5d$ states and (2) the charge anisotropy of the quadrupole ordering $4f$ states modulates the $5d$ states through the $5d$-$4f$ Coulomb interaction. Both processes give rise to the RXS intensities on $(00\frac{\ell}{2})$ and $(h0\frac{\ell}{2})$ spots. Both give similar photon-energy dependences and the same azimuthal-angle dependences for the main peak, in agreement with the experiment. The first process is found to give the intensities much larger than the second one in a wide parameter range of crystal field. This suggests that the main-peak of the RXS spectra is not a direct reflection of the quadrupole order but mainly controlled by the lattice distortion.Comment: 8 pages, 8 figures, Latex, To be published in J. Phys. Soc. Jp

Orthorhombic distortion and orbital order in the vanadium spinel FeV2 O4

Using synchrotron and neutron diffraction measurements, we find a low-temperature orthorhombic phase in vanadium spinel FeV2O4. The orbital order of V3+ ions with tetragonal normal modes occurs at 68 K, and this leads to an appearance of the pseudotetragonal phase at a noncollinear ferrimagnetic transition temperature. Below the magnetic transition temperature, unconventional behavior of the orbital state of Fe2+ ions accompanied by the emergence of the orthorhombic phase was observed by using the normal mode analysis. We have also studied the structural properties of orbitally diluted materials. The orthorhombic phase, which is significantly affected by the other ions, is intrinsic in FeV2O4. We suggest the orthorhombic phase is strongly related with the double orbital states of Fe2+ and V3+ ions

STOCHASTIC DYNAMICS OF LARGE-SCALE INFLATION IN DE~SITTER SPACE

In this paper we derive exact quantum Langevin equations for stochastic dynamics of large-scale inflation in de~Sitter space. These quantum Langevin equations are the equivalent of the Wigner equation and are described by a system of stochastic differential equations. We present a formula for the calculation of the expectation value of a quantum operator whose Weyl symbol is a function of the large-scale inflation scalar field and its time derivative. The unique solution is obtained for the Cauchy problem for the Wigner equation for large-scale inflation. The stationary solution for the Wigner equation is found for an arbitrary potential. It is shown that the large-scale inflation scalar field in de Sitter space behaves as a quantum one-dimensional dissipative system, which supports the earlier results. But the analogy with a one-dimensional model of the quantum linearly damped anharmonic oscillator is not complete: the difference arises from the new time dependent commutation relation for the large-scale field and its time derivative. It is found that, for the large-scale inflation scalar field the large time asymptotics is equal to the `classical limit'. For the large time limit the quantum Langevin equations are just the classical stochastic Langevin equations (only the stationary state is defined by the quantum field theory).Comment: 21 pages RevTex preprint styl