Multicritical point in a diluted bilayer Heisenberg quantum antiferromagnet

The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed interlayer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multicritical point (p(*),g(*)) at the classical percolation density p=p(*) and interlayer coupling g(*) approximately equal 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero interlayer coupling and could be relevant for antiferromagnetic cuprates doped with nonmagnetic impurities.     

Quantum criticality and percolation in dimer-diluted two-dimensional antiferromagnets

The S = 1/2 Heisenberg model is considered on bilayer and single-layer square lattices with couplings J1, J2, with each spin belonging to one J2-coupled dimer. A transition from a Néel to disordered ground state occurs at a critical value of g = J2/J1. The systems are here studied at their dimer-dilution percolation points p*. The multicritical point (g*,p*) previously found for the bilayer is not reproduced for the single layer. Instead, there is a line of critical points (g < g*, p*) with continuously varying exponents. The uniform magnetic susceptibility diverges as T(-alpha) with alpha element of [1/2,1]. This unusual behavior is attributed to an effective free-moment density approximately T(1-alpha). The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.     

Measuring the P-odd pion-nucleon coupling h((1))(piNN) in pi(+)-photoproton production near threshold

We show that gamma-->p-->pi(+)n in the threshold region is an excellent candidate for measuring the leading parity-violating pion-nucleon coupling h((1))(piNN) to an uncertainty of 20% if it has a natural size from dimensional analysis. The conclusion is based on a large unpolarized cross section, a new low-energy theorem for the photon polarization asymmetry at the threshold A(gamma)/(th) = square root of 2 f(pi)(mu(p)-mu(n))h((1))(piNN)/g(A)m(N) approximately h((1))(piNN)/2, and its strong dominance at forward and backward angles in the threshold region.     

Superscaling of percolation on rectangular domains

For percolation on (RL)xL two-dimensional rectangular domains with a width L and aspect ratio R, we propose that the existence probability of the percolating cluster E(p)(L,epsilon,R) as a function of L, R, and deviation from the critical point epsilon can be expressed as F(epsilonL(y(t))R(a)), where y(t) identical with1/nu is the thermal scaling power, a is a new exponent, and F is a scaling function. We use Monte Carlo simulation of bond percolation on square lattices to test our proposal and find that it is well satisfied with a=0.14(1) for R>2. We also propose superscaling for other critical quantities.     

Percolation of diffusional creep: a new universality class

We study the percolation aspects of diffusional "Coble" creep on heterogeneous grain boundary networks, assuming free grain boundary sliding. A novel percolation threshold is obtained for the honeycomb lattice when two representative types of grain boundaries are randomly distributed, p(cc)=0.5416+/-0.0036. The creep viscosity diverges near the percolation threshold with power-law exponents t=1.69+/-0.09 and s=1.88+/-0.12, different from the standard conduction and rigidity percolation exponents. The moments of both the force and flux distributions all conform to finite-size scaling at p(cc), but with new exponents. These new scaling behaviors seen in the creeping system are proposed to arise from the unique coupling of both force and flux balances in the network.     

Percolation phenomenon of calcium bis(2-ethylhexyl) sulfosuccinate water-in-oil microemulsions by conductivity and dielectric spectroscopy measurements

The sodium counterion (Na+) of the sodium bis(2-ethylhexyl) sulfosuccinate (AOT) surfactant was exchanged with calcium Ca2+ to investigate the counterion charge effect on the structure of water in normal decane microemulsions. Ohmic conductivity and dielectric permittivity measurements were performed on samples at constant water to surfactant mole ratio [water]/[Ca(AOT)(2)]=26.6. Increasing the volume fraction of the dispersed phase phi, a percolation phenomenon was observed at the constant temperature of 25 degrees C. The percolation threshold was found at phi approximately 15% by Ohmic conductivity and static dielectric permittivity studied as a function of phi, and by the frequency dependence of the complex permittivity. Critical exponents typical of the static percolation mechanism (formation of bicontinuous microemulsions) were found below and above threshold. The comparison of these results obtained for the two different counterions, Ca2+ and Na+, in AOT surfactant water in normal decane microemulsions allows detection of an important difference. The percolation below threshold is dynamic for the sodium-based microemulsions, accounting for the formation of clusters of droplets, whereas calcium-based microemulsions show a static percolation. For this system, the coalescence of droplets begins to occur below threshold at phi approximately 12%.     

Clique percolation in random networks

The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Rényi graph of N vertices we obtain that the percolation transition of k-cliques takes place when the probability of two vertices being connected by an edge reaches the threshold p(c) (k) = [(k - 1)N](-1/(k - 1)). At the transition point the scaling of the giant component with N is highly nontrivial and depends on k. We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.     

Dynamic properties of a diluted pyrochlore cooperative paramagnet (Tb(p)Y(1-p))2Ti2O7

Investigations of the spin dynamics of the geometrically frustrated pyrochlore (Tb(p)Y(1-p))2Ti2O7, using muon spin relaxation and neutron spin echo, as a function of magnetic coverage p, have been carried out. Our major finding is that paramagnetic fluctuations prevail as T-->0 for all values of p, and that they are sensitive to dilution, indicating a cooperative spin motion. However, the percolation threshold pc is not a critical point for the fluctuations. We also find that the low temperature spectral density has a 1/f behavior, and that dilution slows down the spin fluctuations.     

Cluster analysis and finite-size scaling for Ising spin systems

Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction (c) of lattice sites in percolating clusters in subgraphs with n percolating clusters, f(n)(c), and the distribution function for magnetization (m) in subgraphs with n percolating clusters, p(n)(m). We find that f(n)(c) and p(n)(m) have very good finite-size scaling behavior and that they have universal finite-size scaling functions for the model on square, plane triangular, and honeycomb lattices when aspect ratios of these lattices have the proportions 1:square root[3]/2:square root[3]. The complex structure of the magnetization distribution function p(m) for the system with large aspect ratio could be understood from the independent orientations of two or more percolation clusters in such a system.     

Percolation quantum phase transitions in diluted magnets

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.     

Anomalous enhancement of the coupling to the magnetic resonance mode in underdoped Pb-Bi2212

High-resolution angle-resolved photoemission with variable excitation energies is used to disentangle bilayer splitting effects and intrinsic (self-energy) effects in the electronic spectral function near the (pi,0) point of differently doped (Pb,Bi)(2)Sr(2)CaCu(2)O(8+delta). In contrast to overdoped samples, where intrinsic effects at the (pi,0) point are virtually absent, we find in underdoped samples intrinsic effects in the superconducting-state (pi,0) spectra of the antibonding band. This intrinsic effect is present only below the critical temperature and weakens considerably with doping. Our results give strong support for models which involve a strong coupling of electronic excitations with the resonance mode seen in inelastic neutron scattering experiments.     

Percolation—related magnetic coupling and magnetoresistance properties in Fe／Si1—xAgx multilayers

In this paper, we present a study of the magnetic coupling and magnetoresistance (MR) properties in Fe/Si_1-xAg_x multilayers with a granular Si_1-xAg_x spacer layer. We have found that, with increasing silver content (x) in a silicon matrix, the magnetic state of multilayers changes from a nonmagnetic coupling state to weak antiferromagnetic around the percolation point of the ～2.4 nm thick spacer Si_1-xAg_x. The MR measurements also reveal an abrupt increase of MR near the same percolation point. These changes are ascribed to the formation of the percolation path in the granular spacer.     

Quantum localization in bilayer Heisenberg antiferromagnets with site dilution

The field-induced antiferromagnetic ordering in systems of weakly coupled S = 1/2 dimers at zero temperature can be described as a Bose-Einstein condensation of triplet quasiparticles (singlet quasiholes) in the ground state. For the case of a Heisenberg bilayer, it is here shown how the above picture is altered in the presence of site dilution of the magnetic lattice. Geometric randomness leads to quantum localization of the quasiparticles or quasiholes and to an extended Bose-glass phase in a realistic disordered model. This localization phenomenon drives the system towards a quantum-disordered phase well before the classical geometric percolation threshold is reached.     

Percolation analysis of stochastic models of galactic evolution

The stochastic star formation model of galactic evolution can be cast as a problem of directed percolation, the time dimension being that along which the directed bonds exist. We study various aspects of this percolation, those of general interest for the percolation phase transition and those of particular importance for the astrophysical application. Both analytical calculations and computer simulations are provided and the results compared. Among the properties are: value of the percolation threshold, critical indices, percolation probability (star density) near and away from the critical point, local density, cluster sizes, effects of rotation (for disk galaxy models) on the percolation threshold. Astrophysical consequences of some of these properties are discussed, in particular the way in which general phase transition behavior contributes to spiral arm morphology. We look at 1 (space) + 1 (time), 2 + 1 and + 1 dimensions, the 2 + 1 case being of interest for disk galaxies.     

First-Passage Percolation, Semi-Directed Bernoulli Percolation, and Failure in Brittle Materials

We present a two-dimensional, quasistatic model of fracture in disordered brittle materials that contains elements of first-passage percolation, i.e., we use a minimum-energy-consumption criterion for the fracture path. The first-passage model is employed in conjunction with a semi-directed Bernoulli percolation model, for which we calculate critical properties such as the correlation length exponent v ^sdir and the percolation threshold p _c ^sdir . Among other results, our numerics suggest that v ^sdir is exactly 3/2, which lies between the corresponding known values in the literature for usual and directed Bernoulli percolation. We also find that the well-known scaling relation between the wandering and energy fluctuation exponents breaks down in the vicinity of the threshold for semi-directed percolation. For a restricted class of materials, we study the dependence of the fracture energy (toughness) on the width of the distribution of the specific fracture energy and find that it is quadratic in the width for small widths for two different random fields, suggesting that this dependence may be universal.     

Structural transition and metallization in liquid selenium

The insulator-metal transitions of different kinds caused by heating above the melting temperature under pressure of tens kilobars and by compressing at the critical temperature to a pressure of about 1.1 kbar occur in liquid selenium. At tens kilobars, metallization is interpreted as the forbidden energy band vanishing due to a gradual structural transition (melting of polymer chains) described by the Clapeyron-Clausius equation. At supercritical temperatures, the insulator-metal transition is caused by percolation of overlapping electron shells (classically accessible spheres) of virtual atoms in molecules Se₂ remaining when polymer chains decay. The percolation threshold in such a system has been found to increase due to coupling of virtual atoms. The thermally activated conductivity in the vicinity of percolation threshold has been calculated and compared with existing experimental data.     

Measurement of absolute cross sections for excitation of the 3s(2)3p(5) 2P(o)(3/2)- 3s(2)3p(5) 2P(o)(1/2) fine-structure transition in Fe9+

Experimental cross sections are reported for the 3s(2)3p(5) 2P(o)(3/2)- 3s(2)3p(5) 2P(o)(1/2) transition in Fe9+ located at 1.945 eV. The center-of-mass interaction energies are in the range of 1.72 eV (below threshold) through threshold, to 5.6 eV (2.9 x threshold). Data are compared with results of a 49-state Breit-Pauli R-matrix theory. The experiment detects structures at 3.5 and 4.6 eV corresponding to enhancement of the direct excitation via many narrow, closely spaced resonances about these energies calculated by the theory. Iron is present in practically every astrophysical object, as well as being an impurity in fusion plasmas. Present data are the first electron-energy-loss measurements on a highly charged iron ion.     

Linking numbers for self-avoiding loops and percolation: application to the spin quantum hall transition

Nonlocal twist operators are introduced for the O(n) and Q-state Potts models in two dimensions which count the numbers of self-avoiding loops (respectively, percolation clusters) surrounding a given point. Their scaling dimensions are computed exactly. This yields many results: for example, the number of percolation clusters which must be crossed to connect a given point to an infinitely distant boundary. Its mean behaves as (1/3sqrt[3] pi) |ln( p(c)-p)| as p-->p(c)-. As an application we compute the exact value sqrt[3]/2 for the conductivity at the spin Hall transition, as well as the shape dependence of the mean conductance in an arbitrary simply connected geometry with two extended edge contacts.     

Description of the degree of reinforcement of polymer/carbon nanotube nanocomposites in the framework of percolation models

A radically new percolation model for describing the extremal dependence of the degree of reinforcement of polymer/carbon nanotube nanocomposites on the nanofiller content has been proposed. It has been shown that, for this nanofiller, the percolation threshold almost coincides with the aggregation threshold on the concentration scale. From the structural point of view, the extremum of this dependence is caused by the change in the type of the reinforcing component (from interphase regions to the skeleton of carbon nanotubes). From the mathematical point of view, the behavior of the degree of reinforcement is described by the general percolation relationship with replacement of the critical exponents near the percolation threshold. Neither the functionalization of the nanofiller nor the preliminary ultrasound treatment qualitatively change the dependence under study.     

Microscopic description of an Ising spin glass near the percolation threshold

Monte Carlo results using a microscopic model to describe FexZn(1-x)F2 indicate that its spin-glass phase at x=0.25 and zero magnetic field is characterized by the presence of antiferromagnetic fractal domains, separated by random vacancies and strongly correlated in time. The effective local random-field distribution corroborates this glassy behavior, which emerges irrespective of ab initio competing interactions and is a consequence of the fractal domain structure near the percolation threshold, x(p)=0.24. The aging properties of the system are in agreement with predictions of short-range stochastic spin-glass models and with the droplets model for spin glass close to percolation.