Book Review

Review of: MARY R. ENGLISH, SITING LOW-LEVEL RADIOACTIVE WASTE DISPOSAL FACILITIES: THE PUBLIC POLICY DILEMMA. (Quorum Books 1992) [278 pp.], Appendices, index, introduction, references. LC-91-42774; ISBN 0-89930-560-1. [$49.95 cloth. One Madison Avenue, New York NY 10010.

Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to c0c_0

We prove that a Hilbert space frame \fti contains a Riesz basis if every subfamily \ftj , J \subseteq I , is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements

Weyl-Heisenberg frames for subspaces of L^2(R)

We give sufficient conditions for translates and modulates of a function g in L^2(R) to be a frame for its closed linear span. Even in the case where this family spans all of L^2(R), wou conditions are significantly weaker than the previous known conditions.Comment: 13 page

Magnetic phase diagram of the iron pnictides in the presence of spin-orbit coupling: Frustration between C2C_2 and C4C_4 magnetic phases

We investigate the impact of spin anisotropic interactions, promoted by spin-orbit coupling, on the magnetic phase diagram of the iron-based superconductors. Three distinct magnetic phases with Bragg peaks at $(\pi,0)$ and $(0,\pi)$ are possible in these systems: one $C_2$ (i.e. orthorhombic) symmetric stripe magnetic phase and two $C_4$ (i.e. tetragonal) symmetric magnetic phases. While the spin anisotropic interactions allow the magnetic moments to point in any direction in the $C_2$ phase, they restrict the possible moment orientations in the $C_4$ phases. As a result, an interesting scenario arises in which the spin anisotropic interactions favor a $C_2$ phase, but the other spin isotropic interactions favor a $C_4$ phase. We study this frustration via both mean-field and renormalization-group approaches. We find that, to lift this frustration, a rich magnetic landscape emerges well below the magnetic transition temperature, with novel $C_2$, $C_4$, and mixed $C_2$-$C_4$ phases. Near the putative magnetic quantum critical point, spin anisotropies promote a stable Gaussian fixed point in the renormalization-group flow, which is absent in the spin isotropic case, and is associated with a near-degeneracy between $C_2$ and $C_4$ phases. We argue that this frustration is the reason why most $C_4$ phases in the iron pnictides only appear inside the $C_2$ phase, and discuss additional manifestations of this frustration in the phase diagrams of these materials.Comment: 21 pages, 19 figures, published versio

Emergent magnetic degeneracy in iron pnictides due to the interplay between spin-orbit coupling and quantum fluctuations

Recent experiments in iron pnictide superconductors reveal that, as the putative magnetic quantum critical point is approached, different types of magnetic order coexist over a narrow region of the phase diagram. Although these magnetic configurations share the same wave-vectors, they break distinct symmetries of the lattice. Importantly, the highest superconducting transition temperature takes place close to this proliferation of near-degenerate magnetic states. In this paper, we employ a renormalization group calculation to show that such a behavior naturally arises due to the effects of spin-orbit coupling on the quantum magnetic fluctuations. Formally, the enhanced magnetic degeneracy near the quantum critical point is manifested as a stable Gaussian fixed point with a large basin of attraction. Implications of our findings to the superconductivity of the iron pnictides are also discussed.Comment: 6 pages, 2 figures, published versio