Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices

A conjecture is given for the exact location of the multicritical point in the phase diagram of the +/- J Ising model on the triangular lattice. The result p_c=0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, p_c=0.9327041, again in excellent agreement with a numerical study. The method is a variant of duality transformation to relate the triangular lattice directly with its dual triangular lattice without recourse to the hexagonal lattice, in conjunction with the replica method.Comment: 9 pages, 1 figure; Minor corrections in notatio

High Orbital Eccentricities of Extrasolar Planets Induced by the Kozai Mechanism

One of the most remarkable properties of extrasolar planets is their high orbital eccentricities. Observations have shown that at least 20% of these planets, including some with particularly high eccentricities, are orbiting a component of a wide binary star system. The presence of a distant binary companion can cause significant secular perturbations to the orbit of a planet. In particular, at high relative inclinations, a planet can undergo a large-amplitude eccentricity oscillation. This so-called "Kozai mechanism" is effective at a very long range, and its amplitude is purely dependent on the relative orbital inclination. In this paper, we address the following simple question: assuming that every host star with a detected giant planet also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, how well could secular perturbations reproduce the observed eccentricity distribution of planets? Our calculations show that the Kozai mechanism consistently produces an excess of planets with very high (e >0.6) and very low (e < 0.1) eccentricities. The paucity of near-circular orbits in the observed sample cannot be explained solely by the Kozai mechanism, because, even with high enough inclinations, the Kozai mechanism often fails to produce significant eccentricity perturbations when there are other competing sources of orbital perturbations on secular timescales, such as general relativity. On the other hand, the Kozai mechanism can produce many highly eccentric orbits. Indeed the overproduction of high eccentricities observed in our models could be combined with plausible circularizing mechanisms (e.g., friction from residual gas) to create more intermediate eccentricities (e=0.1-0.6).Comment: 24 pages, 6 figures, ApJ, in press, minor changes to reflect the accepted versio

Statistical mechanical analysis of the linear vector channel in digital communication

A statistical mechanical framework to analyze linear vector channel models in digital wireless communication is proposed for a large system. The framework is a generalization of that proposed for code-division multiple-access systems in Europhys. Lett. 76 (2006) 1193 and enables the analysis of the system in which the elements of the channel transfer matrix are statistically correlated with each other. The significance of the proposed scheme is demonstrated by assessing the performance of an existing model of multi-input multi-output communication systems.Comment: 15 pages, 2 figure

Could the Ultra Metal-poor Stars be Chemically Peculiar and Not Related to the First Stars?

Chemically peculiar stars define a class of stars that show unusual elemental abundances due to stellar photospheric effects and not due to natal variations. In this paper, we compare the elemental abundance patterns of the ultra metal-poor stars with metallicities [Fe/H] $\sim -5$ to those of a subclass of chemically peculiar stars. These include post-AGB stars, RV Tauri variable stars, and the Lambda Bootis stars, which range in mass, age, binarity, and evolutionary status, yet can have iron abundance determinations as low as [Fe/H] $\sim -5$. These chemical peculiarities are interpreted as due to the separation of gas and dust beyond the stellar surface, followed by the accretion of dust depleted-gas. Contrary to this, the elemental abundances in the ultra metal-poor stars are thought to represent yields of the most metal-poor supernova and, therefore, observationally constrain the earliest stages of chemical evolution in the Universe. The abundance of the elements in the photospheres of the ultra metal-poor stars appear to be related to the condensation temperature of that element; if so, then their CNO abundances suggest true metallicities of [X/H]~ -2 to -4, rather than their present metallicities of [Fe/H] < -5.Comment: Accepted for ApJ. 17 pages, 10 figure

Probing Ion-Ion and Electron-Ion Correlations in Liquid Metals within the Quantum Hypernetted Chain Approximation

We use the Quantum Hypernetted Chain Approximation (QHNC) to calculate the ion-ion and electron-ion correlations for liquid metallic Li, Be, Na, Mg, Al, K, Ca, and Ga. We discuss trends in electron-ion structure factors and radial distribution functions, and also calculate the free-atom and metallic-atom form-factors, focusing on how bonding effects affect the interpretation of X-ray scattering experiments, especially experimental measurements of the ion-ion structure factor in the liquid metallic phase.Comment: RevTeX, 19 pages, 7 figure

Chandra Observation of the Cluster Environment of a WAT Radio Source in Abell 1446

Wide-angle tail (WAT) radio sources are often found in the centers of galaxy clusters where intracluster medium (ICM) ram pressure may bend the lobes into their characteristic C-shape. We examine the low redshift (z=0.1035) cluster Abell 1446, host to the WAT radio source 1159+583. The cluster exhibits possible evidence for a small-scale cluster-subcluster merger as a cause of the WAT radio source morphology. This evidence includes the presence of temperature and pressure substructure along the line that bisects the WAT as well as a possible wake of stripped interstellar material or a disrupted cool core to the southeast of the host galaxy. A filament to the north may represent cool, infalling gas that's contributing to the WAT bending while spectroscopically determined redshifts of member galaxies may indicate some component of a merger occurring along the line-of-sight. The WAT model of high flow velocity and low lobe density is examined as another scenario for the bending of 1159+583. It has been argued that such a model would allow the ram pressure due to the galaxy's slow motion through the ICM to shape the WAT source. A temperature profile shows that the cluster is isothermal (kT= 4.0 keV) in a series of annuli reaching a radius of 400 kpc. There is no evidence of an ongoing cooling flow. Temperature, abundance, pressure, density, and mass profiles, as well as two-dimensional maps of temperature and pressure are presented.Comment: 40 AASTeX pages including 15 postscript figures; accepted for publication in Ap

Duality in finite-dimensional spin glasses

We present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions. The conjecture, in satisfactory agreement with a number of numerical results, was previously derived using an ansatz emerging from duality and the replica method. In the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation. Thus the problem is now clearer than before from a mathematical point of view: The ansatz, somewhat arbitrarily introduced previously, has now been shown to be closely related to the analyticity of a well-defined function.Comment: 12 pages, 3 figures; A reference added; to appear in J. Stat. Phy

Nonexponential decay of an unstable quantum system: Small-QQ-value s-wave decay

We study the decay process of an unstable quantum system, especially the deviation from the exponential decay law. We show that the exponential period no longer exists in the case of the s-wave decay with small $Q$ value, where the $Q$ value is the difference between the energy of the initially prepared state and the minimum energy of the continuous eigenstates in the system. We also derive the quantitative condition that this kind of decay process takes place and discuss what kind of system is suitable to observe the decay.Comment: 17 pages, 6 figure

Graphene-based photonic crystal

A novel type of photonic crystal formed by embedding a periodic array of constituent stacks of alternating graphene and dielectric discs into a background dielectric medium is proposed. The photonic band structure and transmittance of such photonic crystal are calculated. The graphene-based photonic crystals can be used effectively as the frequency filters and waveguides for the far infrared region of electromagnetic spectrum. Due to substantial suppression of absorption of low-frequency radiation in doped graphene the damping and skin effect in the photonic crystal are also suppressed. The advantages of the graphene-based photonic crystal are discussed.Comment: 4 pages, 3 figure