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

Entanglement Entropy in Random Quantum Spin-S Chains

We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin-S. Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude S of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin-3/2 chains using an asymptotically exact real-space renormalization group approach.Comment: 5 pages, 4 figure

Random bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the random bond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter-- and correlation function--probability distribution show a nontrivial scaling near the critical point which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.Comment: RevTeX 13 pages + 4 figures (appended as uuencoded compressed tar-file), THP61-9

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

Quantum Spin Glasses

Ising spin glasses in a transverse field exhibit a zero temperature quantum phase transition, which is driven by quantum rather than thermal fluctuations. They constitute a universality class that is significantly different from the classical, thermal phase transitions. Most interestingly close to the transition in finite dimensions a quantum Griffiths phase leads to drastic consequences for various physical quantities: for instance diverging magnetic susceptibilities are observable over a whole range of transverse field values in the disordered phase.Comment: 10 pages LaTeX (Springer Lecture Notes style file included), 1 eps-figure; Review article for XIV Sitges Conference: Complex Behavior of Glassy System

Entanglement entropy in aperiodic singlet phases

We study the average entanglement entropy of blocks of contiguous spins in aperiodic XXZ chains which possess an aperiodic singlet phase at least in a certain limit of the coupling ratios. In this phase, where the ground state constructed by a real space renormalization group method, consists (asymptotically) of independent singlet pairs, the average entanglement entropy is found to be a piecewise linear function of the block size. The enveloping curve of this function is growing logarithmically with the block size, with an effective central charge in front of the logarithm which is characteristic for the underlying aperiodic sequence. The aperiodic sequence producing the largest effective central charge is identified, and the latter is found to exceed the central charge of the corresponding homogeneous model. For marginal aperiodic modulations, numerical investigations performed for the XX model show a logarithmic dependence, as well, with an effective central charge varying continuously with the coupling ratio.Comment: 18 pages, 9 figure

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse field. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real space renormalization group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the $x$ direction to a ferromagnet in the $y$ direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse field then in a non-zero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground state energy has an essential singularity. The results obtained for the dynamical critical exponent, the typical correlation length, and the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRGDT and numerical work.Comment: 22 pages, RevTeX + epsf, 4 figure

Respostas da capacidade de troca catiônica no perfil do solo após a incorporação de lodo de esgoto.

A utilização de lodo de esgoto para melhorar algumas propriedades físicas, químicas e biológicas do solo, tem sido cada vez mais frequente, pois contém alto teor de matéria orgânica. Sendo que se dispostos de maneira inadequada, podem causar impactos negativos, pois em alguns casos, estão incluídos produtos químicos e metais pesados. O experimento foi realizado em 2005 e tem como objetivo avaliar a CTC em relação à incorporação de dose de lodo de esgoto. O trabalho foi conduzido em campo em uma área experimental. Foram aplicadas cinco doses de lodos: 0, 30, 60, 120 e 240 Mg ha-1, com três repetições em três profundidades 0-10, 10-20 e 20-40 cm. Houve aumento linear da CTC em todas as profundidades quando adicionou-se o lodo de esgoto, sendo que na profundidade de 0-10 cm observou-se um efeito mais acentuado, ou seja, a CTC que era de 2,02 cmolcdm-3, passou para 7,69 cmolcdm-3 quando incorporou 240 Mg ha-1, nas demais profundidades o mesmo pode ser notado, mas com menor elevação da CTC. Na profundidade de 20-40 cm o efeito da incorporação foi bem menor quando comparado com a profundidade de 0-10 cm nas doses semelhantes. A CTC respondeu positivamente a incorporação do lodo de esgoto aumentando à medida que aumenta a dose de lodo incorporado

Random Antiferromagnetic Spin-1/2 Chains with Competing Interactions

We study disordered antiferromagnetic spin-1/2 chains with nearest- and further-neighbor interactions using the real-space renormalization-group method. We find that the system supports two different phases, depending on the ratio of the strength between nearest-neighbor and further-neighbor interactions as well the bond randomness strength. For weak further neighbor coupling the system is in the familiar random singlet phase, while stronger further neighbor coupling drives the system to a large spin phase similar to that found in the study of random antiferromagnetic-ferromagnetic spin chains. The appearance of the large spin phase in the absence of ferromagnetic coupling is due to the frustration introduced by further neighboring couplings, and is unique to the disordered chains.Comment: 11 pages, 7 figure