Random walks in a simple percolation model with two jump frequencies

We consider transport properties of the system in which the good-conducting bonds lie in parallel planes linked by poor-conducting bonds and the concentration p of good-conducting bonds is close to the two-dimensional percolation threshold p_c. The diffusion coefficient D(τ) which describes the random walking in directions along the planes is calculated as a function of variable τ = p − p_c. For τ → 0 the asymptotic relation D(τ)/D(0) − 1 | ∼ |τ|^α is found w α = 2ν − s. Here s is the superconductivity exponent and ν is the correlation length exponent. It is argued that such behavior is to be expected also for more general models.     

Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

The effect of Cu substitution on the A1g mode of La0.7Sr0.3MnO3 manganites

We report on the first Raman data of Cu substituted La_1−ySr_yMn_1−xCu_xO₃ (0≤x≤0.10 and 0.17≤y≤0.3, accordingly in order to have the same Mn⁴⁺/[Mn⁴⁺+Mn³⁺] ratio), collected in the frequency range 100-900 cm⁻¹ and at room temperature, with parallel (e_i∥e_s) and crossed (e_i⊥e_s) polarizations of the incident (e_i) and scattered (e_s) light. Spectra were fitted with a Drude-Lorentz model, and peaks at 190-220 and 430 cm⁻¹, together with two broad structures centered at near 500 and 670 cm⁻¹, have been found. We also have observed that the A_1g mode is substantially shifted with increasing Cu substitution. The A_1g phonon shift is a linear function of the tolerance factor t and the rhombohedral angle α_r, thus following the structural changes of the MnO₆ octahedra in the system.     

A new route to Explosive Percolation

The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the cluster sizes, unlike the power law distribution in AP. In this model single edges between pairs of clusters of sizes s_i and s_j are occupied with a probability ∝(s_is_j)^α. The parameter α is continuously tunable over the entire real axis. Numerical studies indicate that for α<α_c the transition is first order, α_c=0 for a square lattice and α_c=−1/2 for random graphs. In the limits of α=−∞,+∞ this model coincides with models well established in the literature.     

ee Annihilation into two hadrons in the energy interval 1400–2400 MeV

The proof is given for the existence of the reaction e⁺e⁻ → h^±h^? in the energy range 1400–2400 MeV, and its energy dependence is compared with that of e⁺e⁻ → e^±e^?, in the same experimental conditions of observation. The exponent of the s-dependence of the ratio α = (e⁺e⁻ → h^±h^?)/ (e⁺e⁻ → e^±e^?) is measured to be n = 2.08 ± 0.45, in the s-range (1.96 − 5.76) GeV², on the basis of 51 e⁺e⁻ → h^±h^? events and 8918 e⁺e⁻ → e^±e^? events observed.     

Cluster growth poised on the edge of break-up: Size distributions with small exponent power-laws

In many naturally occurring growth processes, cluster size distributions of power-law form n(s)∝s^−τ with small exponents 0<τ<1 are observed. We suggest here that such distributions emerge naturally from cluster growth, where size dependent aggregation is counterbalanced by size dependent break-up. The model used in the study is a simple reaction kinetic model including only monomer-cluster processes. It is shown that under such conditions power-law size distributions with small exponents are obtained. Therefore, the results suggest that the ubiquity of small exponent power-law distributions is related to the growth process, where aggregation driven cluster growth is poised on the edge of cluster break-up.     

Percolation cluster numbers by real-space renormalization

The average numbern _s (p) of percolation clusters withs sites is calculated for the triangular lattice using real-space renormalization. Fors up to 2,000 the whole range of concentrationsp was analyzed;n _s varied over sixty decades. We found logn _s –s forp belowp _c =0.5, andn _s s ^–, =2.35 atp=p _c . For smallp one hasn _s (p · ) ^s . Nearp _c we found the scaling fromn _s s ^– f((p _c –p) ·s ) with=0.53. Presumably for the first time renormalization methods were used to calculate percolation properties not only nearp _c but also far away from the critical point.Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Propagation regimes of intense circularly polarized laser beam in magnetoactive plasma

This paper presents an analytical and numerical investigation of an intense circularly polarized wave propagating along the static magnetic field parallel to oscillating magnetic field in magnetoactive plasma. In the relativistic regime such a magnetic field is created by pulse itself. The authors have studied different regimes of propagation with relativistic electron mass effect for magnetized plasma. An appropriate expression for dielectric tensor in relativistic magnetoactive plasma has been evaluated under paraxial theory. Two modes of propagation as extraordinary and ordinary exist; because of the relativistic effect, ultra-strong magnetic fields are generated which significantly influence the propagation of laser beam in plasma. The nature of propagation is characterized through the critical-divider curves in the normalized beam width with power plane For given values of normalized density (ω_p/ω) and magnetic field (ω_c/ω) the regions are namely steady divergence (SD), oscillatory divergence (OD) and self-focusing (SF). Numerical computations are performed for typical parameters of relativistic laser-plasma interaction: magnetic field B = 10-100 MG; intensity I = 10¹⁶ to 10²⁰ W/cm²; laser frequency ω = 1.1 × 10¹⁵ s⁻¹; cyclotron frequency ω_c = 1.7 × 10¹³ s⁻¹; electron density n_e = 2.18 × 10²⁰ cm⁻³. From the calculations, we confirm that a circularly polarized wave can propagate in different regimes for both the modes, and explicitly indicating enhancement in wave propagation, beam focusing/self-guiding and penetration of E-mode in presence of magnetic field.     

Note on the asymptotic decay of the numbers of percolation clusters

Renormalization group principles are used to argue that the Kunz-Souillard exponents are valid for all concentrations away from the percolation threshold, i.e. that the average numbers n_s of clusters containing s sites each decay as log n_s ∝ -sζ (s → ∞, p fixed), with ζ = 1 for all p below p_c, and ζ = 1 - 1/d for all p above p_c in d dimensions.     

Spin-0 and spin-1/2 particles in a constant scalar-curvature background

We study the Klein-Gordon and Dirac equations in the presence of a background metric ds²=−dt²+dx²+e^−2gx(dy²+dz²) in a semi-infinite lab (x>0). This metric has a constant scalar-curvature R=6g² and is produced by a perfect fluid with equation of state p=−ρ/3. The eigenfunctions of spin-0 and spin-1/2 particles are obtained exactly, and the quantized energy eigenvalues are compared. It is shown that both of these particles must have nonzero transverse momentum in this background. We show that there is a minimum energy E²_min=m²c⁴+g²c²?² for bosons (E_KG>E_min), while the fermions have no specific ground state (E_Dirac>mc²).     

Berezinskii–Kosterlitz–Thouless transition close to the percolation threshold

We use Monte Carlo to investigate the Berezinskii–Kosterlitz–Thouless transition close to the site percolation threshold in a square lattice. Several thermodynamic quantities are calculated for lattice sizes L×L$L\times L$, from 16<L<640$16<L<640$. Our results are consistent with an infinite order transition for any value of the concentration of magnetic sites. We found that close to the critical percolation concentration, _pc$p_c$ (0.592746), the Berezinskii–Kosterlitz–Thouless transition temperature goes to zero as _TBKT∝(p−_pc)^0.908$T_{\mathit{BKT}}\propto {(p-p_c)}^{0.908}$ and the specific heat behaves as _Tsh∝p^1.133$T_{sh}\propto p^{1.133}$.     

Molecular dynamics and phase transitions in paramagnetic [Mn(H2O)6][SiF6] investigated by H NMR

The temperature dependences of ²H NMR spectra and spin-lattice relaxation time T₁ have been measured for paramagnetic [Mn(H₂O)₆][SiF₆]. The obtained ²H NMR spectra were simulated by considering the quadrupole interaction and paramagnetic shift. The variation of the spectra measured in phase III was explained by the 180° flip of water molecules. The activation energy E_a and the jumping rate at infinite temperature k₀ for the 180° flip of H₂O were obtained as 35 kJ mol⁻¹ and 4×10¹⁴ s⁻¹, respectively. The spectral change in phases I and II was ascribed to the reorientation of [Mn(H₂O)₆]²⁺ around the C₃ axis where the E_a and k₀ values were estimated as 45 kJ mol⁻¹ and 1×10¹³ s⁻¹, respectively. From the almost temperature independent and short T₁ value, the correlation time for electron-spin flip-flops, τ_e, and the exchange coupling constant J were obtained as 3.0×10⁻¹⁰ s and 2.9×10⁻³ cm⁻¹, respectively. The II-III phase transition can be caused by the onset of the jumping motion of [Mn(H₂O)₆]²⁺ around the C₃ axis.     

Cluster numbers by series in directed percolation

Cluster numbersn _s from exact expansions for directed percolation in dimensions 2 to 4 are studied at various probability values. The main considerations as regards the asymptotic behaviour are that: $$(i) n_s \propto \exp ( - const s^Z ) for p< p_c (Z = 1) and p > p_c \left( {Z = 1 - \frac{1}{d}} \right).$$ (ii) at the critical thresholdn _s ～s ^?τ+1, although the data can only be reconciled with existing estimates for the exponent if the scaling ansatz is refined to include a first correction.     

2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L²×h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L²-plane parallel to the film. For thicknesses ranging from h/L=0.01 to h/L=0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L≈0.1. In the finite-size regime (h/L?0.01), the percolation threshold scales as pc(h)−pc3∝h−1/x, the exponent x being compatible with that of the critical exponent of the 3D correlation length, ν₃. The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope νD compatible with 2+ν₂, where ν₂ is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1+1/ν₃. In this regime we also observed a logarithmic dependence of the conductivity exponent on h/L.     

Electrical transport properties of CaMnO3 thermoelectric compound: a theoretical study

The electrical transport coefficients of anti-ferromagnetic CaMnO₃ have been investigated by density functional theory calculation within generalized gradient approximation. The calculated transport coefficients exhibit the anisotropic nature, in agreement with its electronic states. The transport property results reveal the stronger carrier transport along the O1–Mn–O1 plane within the O–Mn–O octahedron, indicating that the Mnd and O1p orbitals are mainly responsible for electrical transport. The maximum power factor values as a function of relaxation time reach 8.4×10²³ Wm⁻¹ K⁻² s⁻¹, 7.9×10²³Wm⁻¹ K⁻² s⁻¹ and 4.9×10²³ Wm⁻¹ K⁻² s⁻¹ within c, a and b direction, respectively. The dimensionless figure of merit ZTxx, ZTyy as well as ZTzz is estimated with 1.28, 0.8 and 1.37 at 1000 K, respectively.     

Exact Relations Between Elastic and Electrical Response of d-Dimensional Percolating Networks with Angle-Bending Forces

Arguments are presented to demonstrate that exact equality relations exist between the critical exponents which characterize the macroscopic conductivity _e and the macroscopic elastic stiffness moduli C _e of percolating systems of any dimensionality. Using the notation _e p ^t , C _e p ^T for the critical behavior of a randomly diluted system slightly above the percolation threshold p _c , (pp–p _c >0) and _e |p|^–s , C _e |p|^–S for the critical behavior of a random mixture of normal and perfectly conducting or normal and perfectly rigid constituents slightly below that threshold, (pp–p _c <0) we show that T=t+2 and S=s, where is the percolation correlation length critical exponent |p|^– (p0).     

Effect of pseudogap on the positronium in void

In ceramic high-Tc superconductor (Bi, Pb)₂Sr₂Ca₂Cu₃O₇ the anomalies in temperature dependence τ₂(T)-lifetime of positrons trapped by microvoids are observed in Tc-region [V.L. Sedov, S.N. Kuznetsov, O.A. Tsigelnik, N.N. Oleynikov, D.I. Grigorashev, Phys. Lett. A 222 (1996) 455; D. Sanyal, D. Banerjee, U. De, Phys. Rev. B 58 (1998) 15226]. This effect is considered on the basis of the model in which the positrons trapped in microvoids form positronium atoms, interacting with surrounding medium by the processes Ps↔e⁺+e⁻ [V.L. Sedov, O.A. Tsigelnik, Phys. Lett. A 332 (2004) 423]. It is shown that the local density of states of the interacting positronium forms the δ-peak near the lower boundary of the gap 2Δ at ω>−Δ. The conclusion was made that the experimentally observed discontinuous increase τ₂ at the transition of the superconducting phase into pseudogap state is the result of the discontinuous increased weight of the peak at this transition.