Spin-spin Correlation lengths of Bilayer Antiferromagnets

The spin-spin correlation length and the static structure factor for bilayer antiferromagnets, such as YBa$_2$Cu$_3$O$_{6}$, are calculated using field theoretical and numerical methods. It is shown that these quantities can be directly measured in neutron scattering experiments using energy integrated two-axis scan despite the strong intensity modulation perpendicular to the layers. Our calculations show that the correlation length of the bilayer antiferromagnet diverges considerably more rapidly, as the temperature tends to zero, than the correlation length of the corresponding single layer antiferromagnet typified by La$_2$CuO$_4$. This rapid divergence may have important consequences with respect to magnetic fluctuations of the doped superconductors.Comment: This paper supersedes cond-mat/9703138 and contains numerical simulation results to compare against analytical results. 6 pages, 2 postscript figures (embedded), uses EuroPhys.sty and EuroMac

Spectral Anomaly and High Temperature Superconductors

Spectral anomaly for interacting Fermions is characterized by the spectral function $A([k-k_F],\omega)$ satisfying the scaling relation $A(\Lambda^{y_1} [k-k_F],\Lambda^{y_2}\omega)= \Lambda^{y_A}A([k-k_F],\omega)$, where $y_1$, $y_2$, and $y_A$ are the exponents defining the universality class. For a Fermi liquid $y_1=1$, $y_2=1$, $y_A=-1$; all other values of the exponents are termed anomalous. In this paper, an example for which $y_1=1$, $y_2=1$, but $y_A=\alpha-1$ is considered in detail. Attractive interaction added to such a critical system leads to a novel superconducting state, which is explored and its relevance to high temperature cuprate superconductors is discussed.Comment: RevTex, 53 pages (including figures

A cluster expansion approach to exponential random graph models

The exponential family of random graphs is among the most widely-studied network models. We show that any exponential random graph model may alternatively be viewed as a lattice gas model with a finite Banach space norm. The system may then be treated by cluster expansion methods from statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. Since the free energy is the generating function for the expectations of other random variables, this characterizes the structure and behavior of the limiting network in this parameter region.Comment: 15 pages, 1 figur

Observation of Nonlocal Modulation with Entangled Photons

We demonstrate a new type of quantum mechanical correlation where phase modulators at distant locations, acting on the photons of an entangled pair, interfere to determine the apparent depth of modulation. When the modulators have the same phase, the modulation depth doubles; when oppositely phased, the modulators negate each other.Comment: 4 pages, 4 figure

Criteria for reliable entanglement quantification with finite data

We propose one and a half criteria for determining how many measurements are needed to quantify entanglement reliably. We base these criteria on Bayesian analysis of measurement results, and apply our methods to four-qubit entanglement, but generalizations to more qubits are straightforward.Comment: >4