Molecules with a peptide link in protostellar shocks: a comprehensive study of L1157

Interstellar molecules with a peptide link -NH-C(=O)-, like formamide (NH$_2$CHO), acetamide (NH$_2$COCH$_3$) and isocyanic acid (HNCO) are particularly interesting for their potential role in pre-biotic chemistry. We have studied their emission in the protostellar shock regions L1157-B1 and L1157-B2, with the IRAM 30m telescope, as part of the ASAI Large Program. Analysis of the line profiles shows that the emission arises from the outflow cavities associated with B1 and B2. Molecular abundance of $\approx~(0.4-1.1)\times 10^{-8}$ and $(3.3-8.8)\times 10^{-8}$ are derived for formamide and isocyanic acid, respectively, from a simple rotational diagram analysis. Conversely, NH$_2$COCH$_3$ was not detected down to a relative abundance of a few $\leq 10^{-10}$. B1 and B2 appear to be among the richest Galactic sources of HNCO and NH$_2$CHO molecules. A tight linear correlation between their abundances is observed, suggesting that the two species are chemically related. Comparison with astrochemical models favours molecule formation on ice grain mantles, with NH$_2$CHO generated from hydrogenation of HNCO.Comment: 11 pages, 9 figures. Accepted for publication in MNRAS Main Journal. Accepted 2014 August 19, in original form 2014 July

Ising Spin Glass in a Transverse Magnetic Field

We study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under Renormalisation Group transformations. The phase diagram (critical temperature $T_c$ {\em vs} transverse field $\Gamma$) we obtain shows a finite slope near $T=0$, in contrast with the infinite slope for the pure case. Our results compare very well with the experimental data recently obtained for the dipolar Ising spin glass LiHo$_{0.167}$Y$_{0.833}$F$_4$, in a transverse field. This indicates that this system is more apropriately described by a model with short range interactions than by an equivalent Sherrington-Kirkpatrick model in a transverse field.Comment: 7 pages, RevTeX3, Nota Cientifica PUC-Rio 23/9

Spin-3/2 random quantum antiferromagnetic chains

We use a modified perturbative renormalization group approach to study the random quantum antiferromagnetic spin-3/2 chain. We find that in the case of rectangular distributions there is a quantum Griffiths phase and we obtain the dynamical critical exponent $Z$ as a function of disorder. Only in the case of extreme disorder, characterized by a power law distribution of exchange couplings, we find evidence that a random singlet phase could be reached. We discuss the differences between our results and those obtained by other approaches.Comment: 4 page

Phase diagram of the random Heisenberg antiferromagnetic spin-1 chain

We present a new perturbative real space renormalization group (RG) to study random quantum spin chains and other one-dimensional disordered quantum systems. The method overcomes problems of the original approach which fails for quantum random chains with spins larger than S=1/2. Since it works even for weak disorder we are able to obtain the zero temperature phase diagram of the random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We find a random singlet phase for strong disorder and as disorder decreases, the system shows a crossover from a Griffiths to a disordered Haldane phase.Comment: 4 pages, 10 figure

Role of Disorder on the Quantum Critical Point of a Model for Heavy Fermions

A zero temperature real space renormalization group (RG) approach is used to investigate the role of disorder near the quantum critical point (QCP) of a Kondo necklace (XY-KN) model. In the pure case this approach yields $J_{c}=0$ implying that any coupling $J \not = 0$ between the local moments and the conduction electrons leads to a non-magnetic phase. We also consider an anisotropic version of the model ($X-KN$), for which there is a quantum phase transition at a finite value of the ratio between the coupling and the bandwidth, $(J/W)$. Disorder is introduced either in the on-site interactions or in the hopping terms. We find that in both cases randomness is irrelevant in the $X-KN$ model, i.e., the disorder induced magnetic-non-magnetic quantum phase transition is controlled by the same exponents of the pure case. Finally, we show the fixed point distributions $P_{J}(J/W)$ at the atractors of the disordered, non-magnetic phases.Comment: 5 pages, 3 figure

Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets

It is conjectured that the Haldane phase of the S=1 antiferromagnetic Heisenberg chain and the $S=1/2$ ferromagnetic-antiferromagnetic alternating Heisenberg chain is stable against any strength of randomness, because of imposed breakdown of translational symmetry. This conjecture is confirmed by the density matrix renormalization group calculation of the string order parameter and the energy gap distribution.Comment: 4 Pages, 7 figures; Considerable revisions are made in abstract and main text. Final accepted versio

Rapid Suppression of the Spin Gap in Zn-doped CuGeO_3 and SrCu_2O_3

The influence of non-magnetic impurities on the spectrum and dynamical spin structure factor of a model for CuGeO$_3$ is studied. A simple extension to Zn-doped ${\rm Sr Cu_2 O_3}$ is also discussed. Using Exact Diagonalization techniques and intuitive arguments we show that Zn-doping introduces states in the Spin-Peierls gap of CuGeO$_3$. This effect can beunderstood easily in the large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins, which interact with each other through very weak effective antiferromagnetic couplings. When the dimerization is small, a similar effect is observed but now with the free S=1/2 spins being the resulting S=1/2 ground state of severed chains with an odd number of sites. Experimental consequences of these results are discussed. It is interesting to observe that the spin correlations along the chains are enhanced by Zn-doping according to the numerical data presented here. As recent numerical calculations have shown, similar arguments apply to ladders with non-magnetic impurities simply replacing the tendency to dimerization in CuGeO$_3$ by the tendency to form spin-singlets along the rungs in SrCu$_2$O$_3$.Comment: 7 pages, 8 postscript figures, revtex, addition of figure 8 and a section with experimental predictions, submmited to Phys. Rev. B in May 199

Percolation Transition in the random antiferromagnetic spin-1 chain

We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet phase. We study the statistical properties of the percolation clusters by numerical simulations, and we compute exact exponents characterizing the transition by a real-space renormalization group calculation.Comment: 9 pages, 4 encapsulated Postscript figures, REVTeX 3.