Numerical study of the ordering of the +-J XY spin-glass ladder

The properties of the domain-wall energy and of the correlation length are studied numerically for the one-dimensional +-J XY spin glass on the two-leg ladder lattice, focusing on both the spin and the chirality degrees of freedom. Analytic results obtained by Ney-Niftle et al for the same model were confirmed for asymptotically large lattices, while the approach to the asymptotic limit is slow and sometimes even non-monotonic. Attention is called to the occurrence of the SO(2)-Z_2 decoupling and its masking in spin correlations, the latter reflecting the inequality between the SO(2) and Z_2 exponents. Discussion is given concerning the behaviors of the higher-dimensional models.Comment: 14 pages, 10 figure

Scaling Behaviors of Branched Polymers

We study the thermodynamic behavior of branched polymers. We first study random walks in order to clarify the thermodynamic relation between the canonical ensemble and the grand canonical ensemble. We then show that correlation functions for branched polymers are given by those for $\phi^3$ theory with a single mass insertion, not those for the $\phi^3$ theory themselves. In particular, the two-point function behaves as $1/p^4$, not as $1/p^2$, in the scaling region. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is four.Comment: 17 pages, 3 figure

Large-scale Filamentary Structure around the Protocluster at Redshift z=3.1

We report the discovery of a large-scale coherent filamentary structure of Lyman alpha emitters in a redshift space at z=3.1. We carried out spectroscopic observations to map the three dimensional structure of the belt-like feature of the Lyman alpha emitters discovered by our previous narrow-band imaging observations centered on the protocluster at z=3.1. The feature was found to consist of at least three physical filaments connecting with each other. The result is in qualitative agreement with the prediction of the 'biased' galaxy-formation theories that galaxies preferentially formed in large-scale filamentary or sheet-like mass overdensities in the early Universe. We also found that the two known giant Lyman alpha emission-line nebulae showing high star-formation activities are located near the intersection of these filaments, which presumably evolves into a massive cluster of galaxies in the local Universe. This may suggest that massive galaxy formation occurs at the characteristic place in the surrounding large-scale structure at high redshift.Comment: 11 pages, 3 figures, accepted for publication in ApJ Letter