Parisi States in a Heisenberg Spin-Glass Model in Three Dimensions

We have studied low-lying metastable states of the $\pm J$ Heisenberg model in two ($d=2$) and three ($d=3$) dimensions having developed a hybrid genetic algorithm. We have found a strong evidence of the occurrence of the Parisi states in $d=3$ but not in $d=2$. That is, in $L^d$ lattices, there exist metastable states with a finite excitation energy of $\Delta E \sim O(J)$ for $L \to \infty$, and energy barriers $\Delta W$ between the ground state and those metastable states are $\Delta W \sim O(JL^{\theta})$ with $\theta > 0$ in $d=3$ but with $\theta < 0$ in $d=2$. We have also found droplet-like excitations, suggesting a mixed scenario of the replica-symmetry-breaking picture and the droplet picture recently speculated in the Ising SG model.Comment: 4 pages, 6 figure

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

Three Dimensional Heisenberg Spin Glass Models with and without Random Anisotropy

We reexamine the spin glass (SG) phase transition of the $\pm J$ Heisenberg models with and without the random anisotropy $D$ in three dimensions ($d = 3$) using complementary two methods, i.e., (i) the defect energy method and (ii) the Monte Carlo method. We reveal that the conventional defect energy method is not convincing and propose a new method which considers the stiffness of the lattice itself. Using the method, we show that the stiffness exponent $\theta$ has a positive value ($\theta > 0$) even when $D = 0$. Considering the stiffness at finite temperatures, we obtain the SG phase transition temperature of $T_{\rm SG} \sim 0.19J$ for $D = 0$. On the other hand, a large scale MC simulation shows that, in contrary to the previous results, a scaling plot of the SG susceptibility $\chi_{\rm SG}$ for $D = 0$ is obtained using almost the same transiton temperature of $T_{\rm SG} \sim 0.18J$. Hence we believe that the SG phase transition occurs in the Heisenberg SG model in $d = 3$.Comment: 15 pages, 9 figures, to be published in J. Phys.

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