Phase diagrams and universality classes of random antiferromagnetic spin ladders

The random antiferromagnetic two-leg and zigzag spin-1/2 ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin-1/2 chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the latter system is never realized. We find, however, a new universal fixed point at intermediate disorder.Comment: 10 pages, 10 figure

Valence-bond theory of highly disordered quantum antiferromagnets

We present a large-N variational approach to describe the magnetism of insulating doped semiconductors based on a disorder-generalization of the resonating-valence-bond theory for quantum antiferromagnets. This method captures all the qualitative and even quantitative predictions of the strong-disorder renormalization group approach over the entire experimentally relevant temperature range. Finally, by mapping the problem on a hard-sphere fluid, we could provide an essentially exact analytic solution without any adjustable parameters.Comment: 5 pages, 3 eps figure

Strong-disorder renormalization-group study of the one-dimensional tight-binding model

We formulate a strong-disorder renormalization-group (SDRG) approach to study the beta function of the tight-binding model in one dimension with both diagonal and off-diagonal disorder for states at the band center. We show that the SDRG method, when used to compute transport properties, yields exact results since it is identical to the transfer matrix method. The beta function is shown to be universal when only off-diagonal disorder is present even though single-parameter scaling is known to be violated. A different single-parameter scaling theory is formulated for this particular (particle-hole symmetric) case. Upon breaking particle-hole symmetry (by adding diagonal disorder), the beta function is shown to crossover from the universal behavior of the particle-hole symmetric case to the conventional non-universal one in agreement with the two-parameter scaling theory. We finally draw an analogy with the random transverse-field Ising chain in the paramagnetic phase. The particle-hole symmetric case corresponds to the critical point of the quantum Ising model while the generic case corresponds to the Griffiths paramagnetic phase.Comment: includes 12 pages, 4 figure

Unveiling shocks in planetary nebulae

The propagation of a shock wave into a medium is expected to heat the material beyond the shock, producing noticeable effects in intensity line ratios such as [O III]/Halpha. To investigate the occurrence of shocks in planetary nebulae (PNe), we have used all narrowband [O III] and Halpha images of PNe available in the HST archive to build their [O III]/Halpha ratio maps and to search for regions where this ratio is enhanced. Regions with enhanced [O III]/Halpha emission ratio can be ascribed to two different types of morphological structures: bow-shock structures produced by fast collimated outflows and thin skins enveloping expanding nebular shells. Both collimated outflows and expanding shells are therefore confirmed to generate shocks in PNe. We also find regions with depressed values of the [O III]/Halpha ratio which are found mostly around density bounded PNe, where the local contribution of [N II] emission into the F656N Halpha filter cannot be neglected.Comment: 13 pages, 9 figures, 3 tables; To appear in Astronomy & Astrophysic