Universality of liquid-gas Mott transitions at finite temperatures

We explain in a consistent manner the set of seemingly conflicting experiments on the finite temperature Mott critical point, and demonstrate that the Mott transition is in the Ising universality class. We show that, even though the thermodynamic behavior of the system near such critical point is described by an Ising order parameter, the global conductivity can depend on other singular observables and, in particular, on the energy density. Finally, we show that in the presence of weak disorder the dimensionality of the system has crucial effects on the size of the critical region that is probed experimentally.Comment: 4 pages, 3 figure

Excitations and Quantum Fluctuations in Site Diluted Two-Dimensional Antiferromagnets

We study the effect of site dilution and quantum fluctuations in an antiferromagnetic spin system on a square lattice within the linear spin-wave approximation. By performing numerical diagonalization in real space and finite-size scaling, we characterize the nature of the low-energy spin excitations for different dilution fractions up to the classical percolation threshold. We find nontrivial signatures of fractonlike excitations at high frequencies. Our simulations also confirm the existence of an upper bound for the amount of quantum fluctuations in the ground state of the system, leading to the persistence of long-range order up to the percolation threshold. This result is in agreement with recent neutron-scattering experimental data and quantum Monte Carlo numerical calculations. We also show that the absence of a quantum critical point below the classical percolation threshold holds for a large class of systems whose Hamiltonians can be mapped onto a system of coupled noninteracting massless bosons.Comment: RevTex 4, 16 pages, 8 EPS figures, typos corrected, data from Ref. 9 added, few minor changes in the text, to appear in Phys. Rev.

Site dilution of quantum spins in the honeycomb lattice

We discuss the effect of site dilution on both the magnetization and the density of states of quantum spins in the honeycomb lattice, described by the antiferromagnetic Heisenberg spin-S model. For this purpose a real-space Bogoliubov-Valatin transformation is used. In this work we show that for the S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin S=1/2, however, the linear spin wave approximation breaks down. In this case, we have studied the effect of dilution on the staggered magnetization using the Stochastic Series Expansion Monte Carlo method. Two main results are to be stressed from the Monte Carlo method: (i) a better value for the staggered magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the staggered magnetization of the percolating cluster at the classical percolation threshold, showing that there is no quantum critical transition driven by dilution in the Heisenberg model. In the solution of the problem using linear the spin wave method we pay special attention to the presence of zero energy modes. Using a combination of linear spin wave analysis and the recursion method we were able to obtain the thermodynamic limit behavior of the density of states for both the square and the honeycomb lattices. We have used both the staggered magnetization and the density of states to analyze neutron scattering experiments and Neel temperature measurements on quasi-two- -dimensional honeycomb systems. Our results are in quantitative agreement with experimental results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.Comment: 21 pages (REVTEX), 16 figure

Limited path percolation in complex networks

We study the stability of network communication after removal of $q=1-p$ links under the assumption that communication is effective only if the shortest path between nodes $i$ and $j$ after removal is shorter than $a\ell_{ij} (a\geq1)$ where $\ell_{ij}$ is the shortest path before removal. For a large class of networks, we find a new percolation transition at $\tilde{p}_c=(\kappa_o-1)^{(1-a)/a}$, where $\kappa_o\equiv /$ and $k$ is the node degree. Below $\tilde{p}_c$, only a fraction $N^{\delta}$ of the network nodes can communicate, where $\delta\equiv a(1-|\log p|/\log{(\kappa_o-1)}) < 1$, while above $\tilde{p}_c$, order $N$ nodes can communicate within the limited path length $a\ell_{ij}$. Our analytical results are supported by simulations on Erd\H{o}s-R\'{e}nyi and scale-free network models. We expect our results to influence the design of networks, routing algorithms, and immunization strategies, where short paths are most relevant.Comment: 11 pages, 3 figures, 1 tabl

Double Exchange Model for Magnetic Hexaborides

A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu(1-x)Ca(x)B6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as Hall effect, magnetoresitance, frequency dependent conductivity, and DC resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature, Tc, as a function of the plasma frequency, omega_p.Comment: 4 pages, 3 figure

Probability Distribution of the Shortest Path on the Percolation Cluster, its Backbone and Skeleton

We consider the mean distribution functions Phi(r|l), Phi(B)(r|l), and Phi(S)(r|l), giving the probability that two sites on the incipient percolation cluster, on its backbone and on its skeleton, respectively, connected by a shortest path of length l are separated by an Euclidean distance r. Following a scaling argument due to de Gennes for self-avoiding walks, we derive analytical expressions for the exponents g1=df+dmin-d and g1B=g1S-3dmin-d, which determine the scaling behavior of the distribution functions in the limit x=r/l^(nu) much less than 1, i.e., Phi(r|l) proportional to l^(-(nu)d)x^(g1), Phi(B)(r|l) proportional to l^(-(nu)d)x^(g1B), and Phi(S)(r|l) proportional to l^(-(nu)d)x^(g1S), with nu=1/dmin, where df and dmin are the fractal dimensions of the percolation cluster and the shortest path, respectively. The theoretical predictions for g1, g1B, and g1S are in very good agreement with our numerical results.Comment: 10 pages, 3 figure

Optimal Path and Minimal Spanning Trees in Random Weighted Networks

We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for the minimum distance. For Erd\H{o}s-R\'enyi (ER) and scale free networks (SF), with parameter $\lambda$ ($\lambda >3$), we find that the small-world nature is destroyed. We also find numerically that for weak disorder the length of the optimal path scales logaritmically with the size of the networks studied. We also review the transition between the strong and weak disorder regimes in the scaling properties of the length of the optimal path for ER and SF networks and for a general distribution of weights, and suggest that for any distribution of weigths, the distribution of optimal path lengths has a universal form which is controlled by the scaling parameter $Z=\ell_{\infty}/A$ where $A$ plays the role of the disorder strength, and $\ell_{\infty}$ is the length of the optimal path in strong disorder. The relation for $A$ is derived analytically and supported by numerical simulations. We then study the minimum spanning tree (MST) and show that it is composed of percolation clusters, which we regard as "super-nodes", connected by a scale-free tree. We furthermore show that the MST can be partitioned into two distinct components. One component the {\it superhighways}, for which the nodes with high centrality dominate, corresponds to the largest cluster at the percolation threshold which is a subset of the MST. In the other component, {\it roads}, low centrality nodes dominate. We demonstrate the significance identifying the superhighways by showing that one can improve significantly the global transport by improving a very small fraction of the network.Comment: review, accepted at IJB

Adubação de cafeeiro conilon com fertilizante mineral misto granulado, fonte de magnésio, enxofre e micronutrientes

This study aimed to evaluate the influence of the application of magnesium oxide associated with phosphogypsum and micronutrients (zinc and boron) in the form of granular fertilizer on the soil pH, calcium and magnesium in the soil, dry matter production and contents of calcium, magnesium, zinc and boron in plant, in an experiment carried out in a greenhouse. The experimental design was a randomized block with three replicates distributed in a split plot in time, the main plots consisting of six treatments (without fertilization control; N + P + K; phosphogypsum; magnesium oxide; phosphogypsum/MgO (70/30); phosphogypsum/MgO (70/30) + Zn + B); and the split composed of nine sampling periods. The results show higher levels of calcium (1.19 cmolc dm-3), magnesium (1.87 cmolc dm-3) and zinc (7.33 mg dm-3) in the soil for treatments with application of phosphogypsum, granulated phosphogypsum/MgO (70/30) and phosphogypsum/MgO (70/30) + Zn + B respectively. The application of phosphogypsum also shows higher calcium content (89.66 and 27.74 mg/plant leaves and stem, respectively) and higher dry matter production of leaves (11.22 g/plant), stem (5.67 g/plant) and roots (9.88 g/plant). Treatment with granulated phosphogypsum/MgO (70/30) show higher contents of magnesium (33.86 mg/plant), stem (13.36 mg/plant) and roots (62.97 mg/plant). The greatest contents in leaves B (2.83 mg/plant) and stem (0.24 mg/plant) are found in the treatment phosphogypsum/MgO (70/30) + Zn + B.Objetivou-se, neste trabalho, avaliar a influência da aplicação de óxido de magnésio associado ao gesso agrícola e a micronutrientes (zinco e boro), na forma de fertilizante granulado sobre o pH do solo, e os teores de cálcio e magnésio no solo, produção de matéria seca e conteúdo de cálcio, magnésio, zinco e boro na planta, em experimento conduzido em casa de vegetação. O delineamento experimental foi em blocos casualizados, com três repetições, distribuído em um esquema de parcelas subdivididas no tempo, sendo as parcelas principais compostas por seis tratamentos (controle sem adubação; N + P + K; gesso agrícola; óxido de magnésio; gesso/MgO (70/30); gesso/MgO (70/30) + Zn + B; e as subparcelas compostas por nove períodos de amostragem. Os resultados mostraram teores superiores de cálcio (1,19 cmolc dm-3), magnésio (1,87 cmolc dm-3) e zinco (7,33 mg dm-3) no solo para os tratamentos com aplicação de gesso agrícola, granulados gesso/MgO (70/30) e gesso/MgO (70/30) + Zn + B, respectivamente. A aplicação de gesso agrícola também promoveu maiores conteúdos de cálcio (89,66 e 27,74 mg/planta nas folhas e nos caules, respectivamente) e maior produção de matéria seca de folhas (11,22 g/planta), de caules (5,67 g/planta) e de raízes (9,88 g/planta). O tratamento com granulado gesso/MgO (70/30) promoveu maiores conteúdos de Mg nas folhas (33,86 mg/planta), nos caules (13,36 mg/planta) e nas raízes (62,97 mg/planta). Os maiores conteúdos de B nas folhas (2,83 mg/planta) e nos caules (0,24 mg/planta) foram encontrados no tratamento gesso/MgO (70/30) + Zn + B

Multifractal behavior of linear polymers in disordered media

The scaling behavior of linear polymers in disordered media modelled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p_c is studied. All possible SAW configurations of N steps on a single backbone configuration are enumerated exactly. We find that the moments of order q of the total number of SAWs obtained by averaging over many backbone configurations display multifractal behavior, i.e. different moments are dominated by different subsets of the backbone. This leads to generalized coordination numbers \mu_q and enhancement exponents \gamma_q, which depend on q. Our numerical results suggest that the relation \mu_1 = p_ c \mu between the first moment \mu_1 and its regular lattice counterpart \mu is valid.Comment: 11 pages, 12 postscript figures, to be published in Phys. Rev.

From the Top to the Bottom of the Main Sequence: A Complete Mass Function of the Young Open Cluster M35

We present very deep and accurate photometry of the open cluster M35 (VRIc filters). We have covered a region of 27.5x27.5 square arcmin. The data range from Ic=12.5 to 23.5 mag, and the color intervals are 0.4\le(V-I)c\le3.0, 0.5\le(R-I)c\le2.5. Roughly, these values span from 1.6 M_\odot down to the substellar limit. By using the location of the stars on color-magnitude and color-color diagrams, we have selected candidate members of this cluster. We have merged our sample with previously published data and obtained a color-magnitude diagram for the complete stellar population of the cluster, covering the spectral range early B - mid M. The Mass Function increases monotonically, when plotted in a log-log form, until it reaches ~0.8 M_\odot (\alpha=2.59). It remains shallower for less massive stars (\alpha=0.81 for 0.8-0.2 M_\odot), whereas a decrease ins observed for stars close to the substellar regime. The total mass of the cluster is ~1600 M_\odot in the area covered by this study.Comment: Accepted ApJ (Jan 10, 2001 issue