Quantum fidelity approach to the ground state properties of the 1D ANNNI model in a transverse field

In this work we analyze the ground-state properties of the $s=1/2$ one-dimensional ANNNI model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field $B_x$ and the strength of the next-nearest-neighbor interaction $J_2$, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, paramagnetic, floating, $\Braket{2,2}$ phases, and we predict an infinite number of modulated phases in the thermodynamic limit ($L \rightarrow \infty$). The transition lines separating the modulated phases seem to be of second-order, whereas the line between the floating and the $\Braket{2,2}$ phases is possibly of first-order.Comment: 10 pages, 20 figure

Phase transitions in the two-dimensional super-antiferromagnetic Ising model with next-nearest-neighbor interactions

We use Monte Carlo and Transfer Matrix methods in combination with extrapolation schemes to determine the phase diagram of the 2D super-antiferromagnetic (SAF) Ising model with next-nearest-neighbor (nnn) interactions in a magnetic field. The interactions between nearest-neighbor (nn) spins are ferromagnetic along x, and antiferromagnetic along y. We find that for sufficiently low temperatures and fields, there exists a region limited by a critical line of 2nd-order transitions separating a SAF phase from a magnetically induced paramagnetic phase. We did not find any region with either first-order transition or with re-entrant behavior. The nnn couplings produce either an expansion or a contraction of the SAF phase. Expansion occurs when the interactions are antiferromagnetic, and contraction when they are ferromagnetic. There is a critical ratio R_c = 1/2 between nnn- and nn-couplings, beyond which the SAF phase no longer exists.Comment: 12 pages, 10 figure

Breakdown of the perturbative renormalization group for S >= 1 random antiferromagnetic spin chains

We investigate the application of a perturbative renormalization group (RG) method to random antiferromagnetic Heisenberg chains with arbitrary spin size. At zero temperature we observe that initial arbitrary probability distributions develop a singularity at J=0, for all values of spin S. When the RG method is extended to finite temperatures, without any additional assumptions, we find anomalous results for S >= 1. These results lead us to conclude that the perturbative scheme is not adequate to study random chains with S >= 1. Therefore a random singlet phase in its more restrictive definition is only assured for spin-1/2 chains.Comment: 5 pages, 3 figures. To appear in Physical Review

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

Quantum fidelity approach to the ground-state properties of the one-dimensional axial next-nearest-neighbor Ising model in a transverse field

In this work we analyze the ground-state properties of the s =1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field Bx and the strength of the next-nearest-neighbor interaction J2, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and ⟨2,2⟩ phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only occurs for larger magnetic fields. The transition lines separating the modulated phases seem to be of second order, whereas the line between the floating and the ⟨2,2⟩ phases is possibly of first order

Dissociation of the benzene molecule by UV and soft X-rays in circumstellar environment

Benzene molecules, present in the proto-planetary nebula CRL 618, are ionized and dissociated by UV and X-ray photons originated from the hot central star and by its fast wind. Ionic species and free radicals produced by these processes can lead to the formation of new organic molecules. The aim of this work is to study the photoionization and photodissociation processes of the benzene molecule, using synchrotron radiation and time of flight mass spectrometry. Mass spectra were recorded at different energies corresponding to the vacuum ultraviolet (21.21 eV) and soft X-ray (282-310 eV) spectral regions. The production of ions from the benzene dissociative photoionization is here quantified, indicating that C6H6 is more efficiently fragmented by soft X-ray than UV radiation, where 50% of the ionized benzene molecules survive to UV dissociation while only about 4% resist to X-rays. Partial ion yields of H+ and small hydrocarbons such as C2H2+, C3H3+ and C4H2+ are determined as a function of photon energy. Absolute photoionization and dissociative photoionization cross sections have also been determined. From these values, half-life of benzene molecule due to UV and X-ray photon fluxes in CRL 618 were obtained.Comment: The paper contains 8 pages, 9 figures and 4 tables. Accepted to be published on MNRAS on 2008 November 2

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

Quantum fidelity approach to the ground-state properties of the one-dimensional axial next-nearest-neighbor Ising model in a transverse field

In this work we analyze the ground-state properties of the s = 1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field Bx and the strength of the next-nearest-neighbor interaction J2, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and (2,2) phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only occurs for larger magnetic fields. The transition lines separating the modulated phases seem to be of second order, whereas the line between the floating and the (2,2) phases is possibly of first order

GEOGRAPHICAL SYSTEMS IN THE FIRST CENTURY BC: POSIDONIUS’ F 49 E ̶ K AND VITRUVIUS’ ON ARCHITECTURE VI 1. 3 ̶ 13

The article analyses innovative ethno-geographical systems of the first century BC. During Hellenistic times, the science of geography made use of increasingly advanced mathematical and astronomical skills to ensure a scientific basis for the cartographical project; however, this geographical research apparently disregarded the natural and human environments. There is a paradigm change in the referred century. The Stoic Posidonius focuses on the concept of zones found in the early philosophers and finds a compromise between the ‘scientific’ and the ‘descriptive’ geographies. Likewise, Vitruvius conveys a geographical system which associates climatic, somatic, and psychic features