Apparent Clustering of Intermediate-redshift Galaxies as a Probe of Dark Energy

We show the apparent redshift-space clustering of galaxies in redshift range of 0.2--0.4 provides surprisingly useful constraints on dark energy component in the universe, because of the right balance between the density of objects and the survey depth. We apply Fisher matrix analysis to the the Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS), as a concrete example. Possible degeneracies in the evolution of the equation of state (EOS) and the other cosmological parameters are clarified.Comment: 5 pages, 3 figures, Phys.Rev.Lett., replaced with the accepted versio

Phase diagram of a dilute ferromagnet model with antiferromagnetic next-nearest-neighbor interactions

We have studied the spin ordering of a dilute classical Heisenberg model with spin concentration $x$, and with ferromagnetic nearest-neighbor interaction $J_1$ and antiferromagnetic next-nearest-neighbor interaction $J_2$. Magnetic phases at absolute zero temperature $T = 0$ are determined examining the stiffness of the ground state, and those at finite temperatures $T \neq 0$ are determined calculating the Binder parameter $g_L$ and the spin correlation length $\xi_L$. Three ordered phases appear in the $x-T$ phase diagram: (i) the ferromagnetic (FM) phase; (ii) the spin glass (SG) phase; and (iii) the mixed (M) phase of the FM and the SG. Near below the ferromagnetic threshold $x_{\rm F}$, a reentrant SG transition occurs. That is, as the temperature is decreased from a high temperature, the FM phase, the M phase and the SG phase appear successively. The magnetization which grows in the FM phase disappears in the SG phase. The SG phase is suggested to be characterized by ferromagnetic clusters. We conclude, hence, that this model could reproduce experimental phase diagrams of dilute ferromagnets Fe$_x$Au$_{1-x}$ and Eu$_x$Sr$_{1-x}$S.Comment: 9 pages, 23 figure

Ground-State Properties of a Heisenberg Spin Glass Model with a Hybrid Genetic Algorithm

We developed a genetic algorithm (GA) in the Heisenberg model that combines a triadic crossover and a parameter-free genetic algorithm. Using the algorithm, we examined the ground-state stiffness of the $\pm J$ Heisenberg model in three dimensions up to a moderate size range. Results showed the stiffness constant of $\theta = 0$ in the periodic-antiperiodic boundary condition method and that of $\theta \sim 0.62$ in the open-boundary-twist method. We considered the origin of the difference in $\theta$ between the two methods and suggested that both results show the same thing: the ground state of the open system is stable against a weak perturbation.Comment: 11 pages, 5 figure

Ehrenfest theorems for field strength and electric current in Abelian projected SU(2) lattice gauge theory

We derive an Ehrenfest theorem for SU(2) lattice gauge theory which, after Abelian projection, relates the Abelian field strength and a dynamical electric current and defines these operators for finite lattice spacing. Preliminary results from the ongoing numerical test of the relation are presented, including the contributions from gauge fixing and the Faddeev-Popov determinant (the ghost fields) in the maximally Abelian gauge.Comment: 3pp. LaTeX, using espcrc2.sty. Talk presented at Lattice 9

Redshift-space Distortions of the Power Spectrum of Cosmological Objects on a Light Cone : Explicit Formulations and Theoretical Implications

We examine the effects of the linear and the cosmological redshift-space distortions on the power spectrum of cosmological objects on a light cone. We develop theoretical formulae for the power spectrum in linear theory of density perturbations in a rigorous manner starting from first principle corresponding to Fourier analysis. Approximate formulae, which are useful properly to incorporate the redshift-space distortion effects into the power spectrum are derived, and the validity is examined. Applying our formulae to galaxy and quasar samples which roughly match the SDSS survey, we will show how the redshift-space distortions distort the power spectrum on the light cone quantitatively.Comment: 30 pages, Accepted for publication in the Astrophysical Journal Supplement Serie

Ordering of the Heisenberg Spin Glass in High Dimensions

Ordering of the Heisenberg spin glass with the nearest-neighbor Gaussian coupling is investigated by equilibrium Monte Carlo simulations in four and five dimensions. Ordering of the mean-field Heisenberg spin-glass is also studied for comparison. Particular attention is paid to the nature of the spin-glass and the chiral-glass orderings. Our numerical data suggest that, in five dimensions, the model exhibits a single spin-glass transition at a finite temperature, where the spin-glass order accompanying the simultaneous chiral-glass order sets in. In four dimensions, by contrast, the model exhibits a chiral-glass transition at a finite temperature, not accompanying the standard spin-glass order. The critical region associated with the chiral-glass transition, however, is very narrow, suggesting that dimension four is close to the marginal dimensionality.Comment: 18 pages, 12 figure

Spin-Glass and Chiral-Glass Transitions in a ±J\pm J Heisenberg Spin-Glass Model in Three Dimensions

The three-dimensional $\pm J$ Heisenberg spin-glass model is investigated by the non-equilibrium relaxation method from the paramagnetic state. Finite-size effects in the non-equilibrium relaxation are analyzed, and the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility in the infinite-size system are obtained. The finite-time scaling analysis gives the spin-glass transition at $T_{\rm sg}/J=0.21_{-0.02}^{+0.01}$ and the chiral-glass transition at $T_{\rm cg}/J=0.22_{-0.03}^{+0.01}$. The results suggest that both transitions occur simultaneously. The critical exponent of the spin-glass susceptibility is estimated as $\gamma_{\rm sg}= 1.7 \pm 0.3$, which makes an agreement with the experiments of the insulating and the canonical spin-glass materials.Comment: 4 pages, 2 figure

Magnetic Excitations in the Quasi-1D Ising-like Antiferromagnet TlCoCl3_3

Neutron inelastic scattering measurements have been performed in order to investigate the magnetic excitations in the quasi-1D Ising-like antiferromagnet TlCoCl$_3$. We observed the magnetic excitation, which corresponds to the spin-wave excitation continuum corresponding to the domain-wall pair excitation in the 1D Ising-like antiferromagnet. According to the Ishimura-Shiba theory, we analyzed the observed spin-wave excitation, and the exchange constant $2J$ and the anistropy $\epsilon$ were estimated as 14.7 meV and 0.14 in TlCoCl$_3$, respectively.Comment: 2 pages, 3 figures, jpsj2.cls, to be published in J. Phys. Soc. Jpn. Vol.75 (2006) No.