Conductivity exponent in three-dimensional percolation by diffusion based on molecular trajectory algorithm and blind-ant rules

Diffusion on random systems above and at their percolation threshold in three dimensions is carried out by a molecular trajectory method and a simple lattice random walk method, respectively. The classical regimes of diffusion on percolation near the threshold are observed in our simulations by both methods. Our Monte Carlo simulations by the simple lattice random walk method give the conductivity exponent μ/ν=2.32±0.02 for diffusion on the incipient infinite clusters and μ/ν=2.21±0.03 for diffusion on a percolating lattice above the threshold. However, while diffusion is performed by the molecular trajectory algorithm either on the incipient infinite clusters or on a percolating lattice above the threshold, the result is found to be μ/ν=2.26±0.02. In addition, it takes less time step for diffusion based on the molecular trajectory algorithm to reach the asymptotic limit comparing with the simple lattice random walk.     

The Rotational Spectrum of SiHF3 in the Vibrational State υ6=2: Observation of Direct l-Type Resonance Transitions

The υ₆=2 vibrational state of the main isotopomer of trifluorosilane, ²⁸SiHF₃, has been investigated in the centimeter- and millimeter-wave ranges. Rotational spectra following the Δ J=1, Δk=Δ l=0 selection rule have been measured up to J=24 and K=23 and for both values of ∣l∣. Two types of direct l-type resonance transitions induced by the (Δ l=Δk=±2) interaction could be observed by means of waveguide Fourier transform microwave spectroscopy in the range 8-26 GHz: 252 transitions following the Δ J=0, Δl=Δk=±2 selection rule covering values of J=7-39 and G=∣k-l∣ from 1 to 18 and 90 transitions following the Δ J=0, Δl=Δ k=±4 selection rule covering values of J=17-52 and G from 1 to 4. Due to the strong (2,2) resonance, 18 A₁-A₂ splittings of the k=l=±2 states from J=36-53 could also be observed. Accidental near-degeneracies lead to strong perturbations due to Δ (k-l)=±3 interactions, enabling the observation of perturbation-allowed transitions with selection rules k=±3(l=±2)↔±4(±2), ±2(±2), A₊↔ ±1(?2), A₋ and ± 1(0)↔± 6(±2). In a multiple-fit analysis the experimental data have been refined using five reduced forms of the effective Hamiltonian as proposed by Sarka and Harder [J. Mol. Spectrosc.197, 254-261 (1999)]. Parameters up to seventh order have been determined including the axial rotational constant C for both values of ∣l∣ and the vibrational separation of the ∣l∣=0 and 2 states. The unitary equivalence of the determined parameter sets has been demonstrated up to fifth order. Differences of the rotational constants in the various parameter sets have been explained by the theory of reduction. Sign relations of the fitted parameters and general features of the direct l-type resonance spectrum in a υ_t=2 level are discussed.     

Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory

We study the ±J random-plaquette Z₂ gauge model (RPGM) in three spatial dimensions, a three-dimensional analog of the two-dimensional ±J random-bond Ising model (RBIM). The model is a pure Z₂ gauge theory in which randomly chosen plaquettes (occurring with concentration p) have couplings with the “wrong sign” so that magnetic flux is energetically favored on these plaquettes. Excitations of the model are one-dimensional “flux tubes” that terminate at “magnetic monopoles” located inside lattice cubes that contain an odd number of wrong-sign plaquettes. Electric confinement can be driven by thermal fluctuations of the flux tubes, by the quenched background of magnetic monopoles, or by a combination of the two. Like the RBIM, the RPGM has enhanced symmetry along a “Nishimori line” in the p-T plane (where T is the temperature). The critical concentration p_c of wrong-sign plaquettes at the confinement-Higgs phase transition along the Nishimori line can be identified with the accuracy threshold for robust storage of quantum information using topological error-correcting codes: if qubit phase errors, qubit bit-flip errors, and errors in the measurement of local check operators all occur at rates below p_c, then encoded quantum information can be protected perfectly from damage in the limit of a large code block. Through Monte-Carlo simulations, we measure p_c0, the critical concentration along the T=0 axis (a lower bound on p_c), finding p_c0=.0293±.0002. We also measure the critical concentration of antiferromagnetic bonds in the two-dimensional RBIM on the T=0 axis, finding p_c0=.1031±.0001. Our value of p_c0 is incompatible with the value of p_c=.1093±.0002 found in earlier numerical studies of the RBIM, in disagreement with the conjecture that the phase boundary of the RBIM is vertical (parallel to the T axis) below the Nishimori line. The model can be generalized to a rank-r antisymmetric tensor field in d dimensions, in the presence of quenched disorder.     

Primordial inflation and present-day cosmological constant from extra dimensions

A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as ρ _Λ ∼M ⁸/M _P ⁴, where M _P is the Planck scale and M is the weak interaction scale. The model is based on (4+D)-dimensional gravity, with D=2 extra dimensions with radius b(t) curled up at the ADD length scale b ₀=M _P /M ²∼0.1 mm. Vacuum fluctuations in the compactified space perturb b ₀ very slightly, generating a small present-day cosmological constant.The radius of the compactified dimensions is predicted to be b ₀≈k ^1/40.09 mm (or equivalently M≈2.4 TeV/k ^1/8), where the Casimir energy density is k/b ⁴.Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M∼10⁻¹⁷ cm, rolls down its potential to b ₀.     

Critical behavior in Ga-doped manganites La0.75(Sr,Ca)0.25Mn1−xGaxO3 (0≤x≤0.1)

The critical properties of perovskite manganite AMn_1−xGa_xO₃ (A=La_0.75Ca_0.08Sr_0.17, x=0, 0.05 and 0.1) at the ferromagnetic–paramagnetic transition have been analyzed. Experimental results revealed that all samples exhibit a second-order magnetic phase transition. The estimated critical exponents derived from the magnetic data using various techniques such as modified Arrott plot, Kouvel–Fisher method, and critical magnetization isotherms M(T_C, H). The critical exponent values for the undoped compound were found to match well with those predicted for the three-dimensional Heisenberg model (β=355±0.007, γ=1.326±0.002, δ=4.90±0.01). While on non-magnetic Ga substitution it tends towards mean-field with long-range interaction. The mean-field model might be due to the random dilution of the Mn sublattice by non-magnetic ion Ga³⁺ and/or the development of the physical size of the clusters which enhance the dipole–dipole interaction.     

Critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.7Pb0.05Na0.25MnO3

Critical behavior in La_0.7Pb_0.05Na_0.25MnO₃ has been investigated by dc magnetization measurements. Magnetic data indicate that the compound exhibits a continuous (second-order) paramagnetic (PM) to ferromagnetic (FM) phase transition. Estimates of critical exponents yield δ=4.80±0.01, γ=1.296±0.002 and β=0.344±0.007 (consistent with both the predictions for the three-dimensional-Heisenberg model and with those reported for materials when the FM transition is ascribed to the double exchange (DE) mechanism as a major origin) with T_C=334.54±0.08. The critical exponent γ is slightly inferior than predicted from the 3D Heisenberg model. Such a difference may be due, within the context of the quenched disorder, to the presence of some alterations of short-range magnetic order of FM clusters in the PM phase. The temperature variation in the effective exponent (γ_eff) is similar to those for disordered ferromagnets.     

Spin glass behavior and critical analysis across the magnetic phase transition in Gd2CoMnO6: dc magnetization and ac susceptibility study

We report here on critical analysis across magnetic phase transition and spin dynamics in Gd₂CoMnO₆. We found that this material behaves differently below and above the applied magnetic field of 20 kOe. The magnetic phase transition switches from nearly mean-field type to unusual class and T_c shifts towards the high temperature above 20 kOe field. The nature of the magnetic phase transition is explored by carrying out critical analysis at low as well as at high magnetic field. The critical exponents obtained at low field using Kouvel-Fisher method are β = 0.65 (2) γ = 0.90 (2), δ = 2.43 and T_c = 120 K. Apparently, these values of critical exponents appear close to mean-field model. For high field the critical exponents are β = 1.24 (2) γ = 0.64 (5), δ = 1.51 (3) and T_c = 128 K. The critical exponents show significant deviation from any universal class. This switchover in the nature of the magnetic phase transition is unique and not seen in many compounds. The formation of non-Griffiths-like clusters in this compound can be a reason for such unique behavior. Further, ac susceptibility has been measured to understand the spin dynamics in detail. The dispersion of frequency-dependent χ_ac below T_c confirms a spin glass state in this material. The observed value of τ_o and T_o indicate the slow dynamic spin which is caused by co-existence of Co/Mn spin magnetic moments. The magneto-caloric effect is also presented for Gd₂CoMnO₆ in this study. The magnetic study and critical analysis across the phase transition reveal a switchover in the nature of phase transition in this material. A non-Griffiths like cluster formation above T_c is found and dynamic susceptibility study reveals a spin glass state below T_c in Gd₂CoMnO₆.     

Simulation of pedestrian counter-flow with right-moving preference

People prefer to walk on the right-hand side of the road for physical and social reasons. In this paper, pedestrian counter-flow in a channel is simulated with the Cellular Automata (CA) Model, with focus on right-preference. Two types of pedestrians are taken into account, walking leftward and rightward along the channel. Circular and open boundaries are adopted respectively. The right-preference intensity, k, is introduced, defined as the ratio of the right-moving probability to left-moving probability. In simulations, the dynamical transition between fluid and jammed phase is presented. With a fixed k, the critical density is independent of the channel size. According to research results on physiology and sociology [O. Guentuerkuen, Nature 421 (2003) 711; M. Reiss, G. Reiss, Percept. Mot. Skill 85 (1997) 569; M.C. Corballis, Psychol. Rev. 104 (1997) 714], k=1,2,8 have been discussed, and k=8 is satisfied in this work. Furthermore, simulation results are compared with the ideal calculation, and other researchers’ experiments [M. Isobe, T. Adachi, T. Nagatani, Physica A 336 (2004) 638]. It is found that right-preference is effective when the density is below critical. The model is shown to be useful to simulate and analyze this situation numerically.     

Diffusion in three-dimensional random systems at their percolation thresholds

Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt ^k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd ^w is found to be 1/d ^w =0.250±0.003.On leave from I. Institut für Theoretische für Physik, Universität Hamburg, D-2000 Hamburg, Federal Republic of Germany.     

Sub-nanometer distances and cluster shapes in dense hydrogen and in higher levels of hydrogen Rydberg matter by phase-delay spectroscopy

The inter-atomic distances in potassium clusters of Rydberg matter (RM) at excitation levels n _B = 4–8 were recently measured by phase-delay spectroscopy (Holmlid, J Nanopart Res 12: 273, 2010). Excitation levels n _B < 4 with shorter inter-atomic distances exist for hydrogen clusters, and distances down to 140 pm are now measured with this light-scattering method. The clusters studied have maximum dimensions from 0.3 nm up to several tens of nm, often being planar. A weak carbon dioxide laser beam interacts with the clusters in a tunable RM cavity. A strong fringe structure is observed as a function of the end-grating angular position. Delay lengths in the clusters are derived from the fringe structure, corresponding to twice the distance between rows or planes in the clusters. Good agreement with predicted and a few previously measured distances in excitation levels n _B = 1, 2, and 3 is found. Close-packing is the main structure both in planar and 3D clusters. Planar clusters are only observed for n _B = 1 and 3, while 3D clusters are found in excitation levels n _B = 1, 2 and 3. The cluster–cluster distance in stacks of planar clusters for n _B = 2 and 3 is now observed for the first time.     

Critical behavior of long linear k-mers on honeycomb lattices

Monte Carlo (MC) simulations, finite-size scaling and theoretical analysis have been carried out to study the critical behavior of long linear particles of length k (k-mers) on honeycomb lattices. A nematic phase, characterized by a big domain of parallel k-mers, is separated from the isotropic state, by a continuous transition occurring at a finite density θ_c. Our study allowed: (1) to determine the minimum value of k (k_min), which allows the formation of the nematic phase, being k_min=11; (2) to predict the dependence of θ_c on k, being θ_c(k)∝k⁻¹; and (3) to obtain the critical exponents, which indicate that the transition belongs to the 2D three-state Potts universality class.     

Spin-glass-like behavior of uncompensated surface spins in NiO nanoparticulated powder

Nickel oxide nanoparticles successfully synthesized by a polymer precursor method are studied in this work. The analysis of X-ray powder diffraction data provides a mean crystallite size of 22±2 nm which is in a good agreement with the mean size estimated from transmission electron microscopy images. Whereas the magnetization (M) vs. magnetic field (H) curve obtained at 5 K is consistent with a ferromagnetic component which coexists with an antiferromagnetic component, the presence of two peaks in the zero-field-cooled trace suggests the occurrence of two blocking process. The broad maximum at high temperature was associated with the thermal relaxation of uncompensated spins at the particle core and the low temperature peak was assigned to the freeze of surface spins clusters. Static and dynamic magnetic results suggest that the correlations of surface spins clusters show a spin-glass-like behavior below T_g=7.3±0.1 K with critical exponents zν=9.7±0.5 and β=0.7±0.1, which are consistent with typical values reported for spin-glass systems.     

Mössbauer study of CoFeRhO4

CoFeRhO₄ has been studied by Mössbauer spectroscopy and X-ray diffraction. The crystal is found to have a cubic spinel structure with the lattice constant a₀=8.451±0.005 Å. The iron ions are in ferric states. The temperature dependence of the magnetic hyperfine field is analyzed by the Néel theory of ferrimagnetism. The intersublattice superexchange interaction is antiferromagnetic and strong with a strength of J_AB=−12.39k_B while the intrasublattice superexchange interactions are weak with strengths of J_AA=−4.96k_B and J_BB=6.20k_B. As the temperature increases toward the Néel temperature T_N, a systematic line broadening effect in the Mössbauer spectrum is observed and interpreted to originate from different temperature dependences of the magnetic hyperfine fields at various iron sites.     

Effects of finite size and shape on scattering and thermodynamic quantities at 2D Ising critical points

Using recent results by Cardy based on the conformal invariance of critical correlation functions we calculate universal results for scattering functions S(k), susceptibilities, correlation lengths and specific heat correction terms for finite Ising systems in two dimensions with circular and rectangular shapes and free boundary conditions. Our results specify the effect of shape on these quantities at the critical point. In particular, the half-width and lineshape of the scattering function is found to be strongly influenced by geometry. For a circle, S(k) follows the infinite system behavior 1/k^2−η, η = 0.25 only for very large k. For a substantial range of intermediate k values it is well represented by 1/k^2−η_app, with an “apparent” exponent η_app. We also discuss the probable influence of end, edge and domain wall effects on the correlation lengths, susceptibilities and specific heat correction terms. The application of our results to experimental systems and other theoretical models is considered.     

Vibrational study,phase transitions and electrical properties of 4-benzylpyridinium monohydrogenselenate

The title compound C₆H₅CH₂C₅H₄NH⁺·HSeO₄⁻ crystallizes in the orthorhombic system with the space group Pbca and the following unit cell dimensions: a=27.449(5) Å; b=10.821(6) Å and c=8.830(1) Å.The structure consists of infinite parallel two-dimensional planes built of HSeO₄⁻ anions and C₆H₅CH₂C₅H₄NH⁺ cations mutually.Differential scanning calorimetry study on 4-benzylpyridinium monohydrogen-selenate was carried out. A high temperature second order phase transition at 363 K was found and characterized by electric measurements. The Raman of polycrystalline sample has been recorded at different temperature between 297 and 373 K.The conductivity relaxation parameters associated with some H⁺ conduction have been determined from an analysis of the M′′/M′′_max spectrum measured in a wide temperature range. An appearance of the superionic phase transition in 4-BSe is closely related to a liberation or even a rotation increase of HSeO₄⁻ groups with heating.     

A new method for estimating the critical current density of a superconductor from its hysteresis loop

The critical current density J_c of some of the superconducting samples, calculated on the basis of the Bean’s model, shows negative curvature for low magnetic field with a downward bending near H = 0. To avoid this problem Kim’s expression of the critical current density, J_c = k/(H₀ + H), where J_c has positive curvature for all H, has been employed by connecting the positive constants k and H₀ with the features of the hysteresis loop of a superconductor. A relation between the full penetration field H_p and the magnetic field H_min, at which the magnetization is minimum, is obtained from the Kim’s theory. Taking the value of J_c at H = H_p according to the actual loop width, as in the Bean’s theory, and at H = 0 according to an enhanced loop width due to the local internal field, values of k and H₀ are obtained in terms of the magnetization values M⁺(?H_min), M^?(H_min), M⁺(H_p) and M^?(H_p). The resulting method of estimating J_c from the hysteresis loop turns out to be as simple as the Bean’s method.     

Asymptotic correlation functions and FFLO signature for the one-dimensional attractive spin-1/2 Fermi gas

We investigate the long distance asymptotics of various correlation functions for the one-dimensional spin-1/2 Fermi gas with attractive interactions using the dressed charge formalism. In the spin polarized phase, these correlation functions exhibit spatial oscillations with a power-law decay whereby their critical exponents are found through conformal field theory. We show that spatial oscillations of the leading terms in the pair correlation function and the spin correlation function solely depend on ΔkF and 2ΔkF, respectively. Here ΔkF=π(n_↑−n_↓) denotes the mismatch between the Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristics of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Our key observation is that backscattering among the Fermi points of bound pairs and unpaired fermions results in a one-dimensional analog of the FFLO state and displays a microscopic origin of the FFLO nature. Furthermore, we show that the pair correlation function in momentum space has a peak at the point of mismatch between both Fermi surfaces k=ΔkF, which has recently been observed in numerous numerical studies.     

The superconducting energy gap measured by tunneling into quench-condensed germanium-gold

Ge_0.5Au_0.5 films, quenched on a substrate below 2K are superconducting with T_c = 3.10 ± 0.12K, and 2Δ(0)k_BT_c= 3.75 ± 0.1. No phonon structure is visible in the second derivative of the tunnel current.     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

Magnetic properties and magnetic entropy changes of perovskite manganese oxide La0.8-xEuxSr0.2MnO3 (x = 0, 0.075)

Magnetocaloric effect and critical exponent analysis of La_0.8-xEu_xSr_0.2MnO_{3 (}x = 0, 0.075) manganites synthesized via a solid state reaction route have been explored. Rietveld analysis indicates that crystal structure of La_0.8-xEu_xSr_0.2MnO_{3 (}for x = 0.0) is in orthorhombic structure with pbnm space group. After the substitution of Eu, the structure changes from orthorhombic (for x = 0.0) to rhombohedral structure for (x = 0.075) with $\mathrm{R}\overline{3}c$ space group. The T_C is 287 K and 271 K for the samples with x = 0.000 and x = 0.075, respectively, and the magnetic entropy change is 2.76J K ^− 1•kg⁻¹ for x = 0.000 and 3.94J K ^− 1•kg⁻¹ for x = 0.075. The real cooling power (RCP) is 447.7 J•kg⁻¹ for the sample with x = 0.000 and 445 J•kg⁻¹ for the samples with x = 0.075. Both samples show a second order phase transition in the vicinity of T_C. The critical exponents were determined using modified Arrott plots and Kouvel-Fisher methods. The critical behavior of these two samples fit best with the mean field model.