A New Measure of the Clustering of QSO Heavy-Element Absorption-Line Systems

We examine the line-of-sight clustering of QSO heavy-element absorption-line systems, using a new measure of clustering, called the reduced second moment measure, that directly measures the mean over-density of absorbers. While closely related to other second-order measures such as the correlation function or the power spectrum, this measure has a number of distinct statistical properties which make possible a continuous exploration of clustering as a function of scale. From a sample of 352 C IV absorbers with median redshift 2.2, drawn from the spectra of 274 QSOs, we find that the absorbers are strongly clustered on scales from 1 to 20 Mpc. Furthermore, there appears to be a sharp break at 20 Mpc, with significant clustering on scales up to 100 Mpc in excess of that which would be expected from a smooth transition to homogeneity. There is no evidence of clustering on scales greater than 100 Mpc. These results suggest that strong C IV absorbers along a line of sight are indicators of clusters and possibly superclusters, a relationship that is supported by recent observations of ``Lyman break'' galaxies.Comment: 13 pages (LaTex, uses aaspp4.sty and psfig.sty), with 3 encapsulated PostScript figures. To appear in The Astrophysical Journal. Extended new discussion of the statistical properties of the reduced second moment measure, and a new figure highlighting the excess clustering on comoving scales greater than 20 Mp

Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses?

We present a detailed proof of a previously announced result (C.M. Newman and D.L. Stein, Phys. Rev. Lett. v. 84, pp. 3966--3969 (2000)) supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on the infinite square lattice are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show --- much less likely in our opinion --- that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest.Comment: 18 pages (LaTeX); 1 figure; minor revisions; to appear in Commun. Math. Phy