Effects of mass media on opinion spreading in the Sznajd sociophysics model

In this work we consider the influence of mass media in the dynamics of the two-dimensional Sznajd model. This influence acts as an external field, and it is introduced in the model by means of a probability p of the agents to follow the media opinion. We performed Monte Carlo simulations on square lattices with different sizes, and our numerical results suggest a change on the critical behavior of the model, with the absence of the usual phase transition for p>∼0.18. Another effect of the probability p is to decrease the average relaxation times τ, that are log-normally distributed, as in the standard model. In addition, the τ values depend on the lattice size L in a power-law form, τ∼L^α, where the power-law exponent depends on the probability p.     

Virtual levels,mixed valence phase and electronic phase transitions in rare earth compounds

We discuss the influence of the Coulomb interaction between localized and conduction electrons on the properties of magnetic impurities in metals and on electronic phase transitions such as the γ—α—α' transitions in Ce and the insulator—metal transition in SmS. Due to excitonic pairing between ?-holes and s-electrons, similar to that in excitonic insulators, the virtual ?-levels in metals may acquire an extra width, which, in contrast to the width in the Anderson model, depends upon the position of the ?-level, the width being the largest when the ?-level crosses the Fermi-level. This effect stabilizes the intermediate valence phase. As a result, in the Falicov model we get either a gradual phase transition (like that found in SmTe), or a first order one, followed by the intermediate valence phase (SmS), or, which is most interesting, two successive jump-like transitions with a mixed valence in between, similar to the γ—α—α' transitions in Ce. The mixed valence phase is described here as a kind of an “excitonic insulator”. The theory also predicts the correct slopes of the phase equilibrium lines for both Ce and SmS.     

Impact of initial lattice structures on networks generated by traces of random walks

We show that the platform stage of network evolution plays a principal role in the topology of resulting networks generated by short-cuts stimulated by the movements of a random walker, the mechanism of which tends to produce power-law degree distributions. To examine the numerical results, we have developed a statistical method which relates the power-law exponent γ to random properties of the subgraph developed in the platform stage. As a result, we find that an important exponent in the network evolution is α, which characterizes the size of the subgraph in the form V∼t^α, where V and t denote the number of vertices in the subgraph and the time variable, respectively. 2D lattices can impose specific limitations on the walker’s diffusion, which keeps the value of α within a moderate range and provides typical properties of complex networks. 1D and 3D cases correspond to different ends of the spectrum for α, with 2D cases in between. Especially for 2D square lattices, a discontinuous change of the network structure is observed, which varies according to whether γ is greater or less than 2. For 1D cases, we show that emergence of nearly complete subgraphs is guaranteed by α<1/2, although the transient power-law is permitted at low increase rates of edges. Additionally, the model exhibits a spontaneous emergence of highly clustered structures regardless of its initial structure.     

The entropy expression of a Fermi liquid in shielded potential approximation. Application to3He

Using the functional representation of the thermodynamical potential, a simple expression for the entropy of a normal Fermi liquid in shielded potential approximation is derived. The result is valid for arbitrary temperatures above a possible phase transition and contains both Fermi (single-particle) and Bose (collective) contributions. It thus represents an improvement over the quasi-particle approximation. — Applying this result to the fluctuation model of liquid³He, we find a Bose contribution of the orderT ³ logT/Θ from spin fluctuations as well as the usual quasi-particle term.     

Correlation functions in the multiple Ising model coupled to gravity

The model of p Ising spins coupled to 2d gravity, in the form of a sum over planar φ³ graphs, is studied and in particular the two-point and spin-spin correlation functions are considered. We first solve a toy model in which only a partial summation over spin configurations is performed and, using a modified geodesic distance, various correlation functions are determined. The two-point function has a diverging length scale associated with it. The critical exponents are calculated and it is shown that all the standard scaling relations apply. Next the full model is studied, in which all spin configurations are included. Many of the considerations for the toy model apply for the full model, which also has a diverging geometric correlation length associated with the transition to a branched polymer phase. Using a transfer function we show that the two-point and spin-spin correlation functions decay exponentially with distance. Finally, by assuming various scaling relations, we make a prediction for the critical exponents at the transition between the magnetized and branched polymer phases in the full model.     

Fractional Kinetics in Kac–Zwanzig Heat Bath Models

We study a variant of the Kac–Zwanzig model of a particle in a heat bath. The heat bath consists of n particles which interact with a distinguished particle via springs and have random initial data. As n → ∞ the trajectories of the distinguished particle weakly converge to the solution of a stochastic integro-differential equation—a generalized Langevin equation (GLE) with power-law memory kernel and driven by 1/f ^α -noise. The limiting process exhibits fractional sub-diffusive behaviour. We further consider the approximation of non-Markovian processes by higher-dimensional Markovian processes via the introduction of auxiliary variables and use this method to approximate the limiting GLE. In contrast, we show the inadequacy of a so-called fractional Fokker–Planck equation in the present context. All results are supported by direct numerical experiments.     

Phase transition in gauge theories and multiple-point model

The phase transition in the regularized U(1) gauge theory is investigated by using the dual Abelian Higgs model of scalar monopoles. The corresponding-renormalization-group-improved effective potential, analogous to the Coleman-Weinberg one, is considered in the two-loop approximation for β functions, and the phase-transition (critical) dual and nondual couplings are calculated in the U(1) gauge theory. It is shown that the critical value of the renormalized electric fine-structure constant,α _crit≈0.208, obtained in this study agrees with the lattice result for compact QED: α _crit ^lat ≈0.20±0.015. This result and the behavior of α in the vicinity of the phase-transition point are compared with the multiple-point-model prediction for the values of α near the Planck scale. Such a comparison is very encouraging for the multiple point model assuming the existence of the multiple critical point at the Planck scale.     

Intrinsic magnetostriction and phase transitions

A new possibility of first-order magnetic phase transitions in simple systems, based on the concept of intrinsic volume-magnetostriction Ω_s ≡ ? V_n/V_n, is suggested. The net volume V_n is defined as the difference between the total lattice volume and the sum of the individual atomic volumes. A magneto-volume equation of state for the net volume: Ω_s = Q₀η^s with s < 2, as well as the dependence of the effective exchange integral on the long-range order parameter η, are postulated. The value s ? 1.5 accounts well for the experimental values of the critical exponents β and δ, as well as for the deviation from linearity of the Arrott—Belov plots obtained for the ferromagnetic transition metals. The model leads to an order—order transition just below the order—disorder transition, thus providing an explanation for the two experimentally found temperatures, the forromagnetic Curie temperature and the paramagnetic Curie—Weiss temperature.     

Three photon virtual annihilation contributions to positronium hyperfine structure

Three photon virtual annihilation contributions to the positronium hyperfine interval are calculated to order α⁶m(α⁴R_∞). The result is obtained in analytic form and leads to the small value of -0.91 MHz for the contribution to the ground state energy difference from this source.     

Analytic continuation of the effective-range expansion as a method for determining the features of bound states: Application to the 6Li nucleus

The scattering function (effective-range function) for the two-channel elastic scattering of charged particles is used to analyze dα scattering at low energies. In order to construct this function, use is made of various sets of phase shifts and mixing parameter, both those that were obtained by solving Faddeev equations in the three-body (n, p, α) model and those that were deduced from available phaseshift analyses. By means of an analytic continuation of the scattering function to the point of the pole corresponding to the bound state of the ⁶Li nucleus, the values of the vertex constants and asymptotic normalization coefficients are found for the process ⁶Li → α + d. Possible means for refining these results are discussed.     

Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model

Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S^−1.3 for the first layer to gamma distributions p(S)≈S^αexp(−S/S₀) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.     

New type of exact solutions to the generalized Ashkin-Teller model and anisotropic Ising model with spin 3/2

The generalized Ashkin-Teller model involving both biquadratic and bilinear interactions between the Ising subsystems (α and s) and equivalent to the anisotropic Ising model with spin 3/2 is considered. For a certain magnitude of the opposite-sign bilinear interactions along the horizontal and vertical axes of a square lattice, the exact analytic solution is obtained that describes the phase transition between the disordered (〈α 〉=〈s〉=〈αs〉=0) and the correlated ordered (〈s〉 ≠0 and 〈α〉=〈s〉=0) states.     

Field-theoretic treatment of the 2d planar model with random p-fold symmetry-breaking field

It is shown that the effects of a random p-fold symmetry-breaking field on the two-dimensional planar model can be studied systematically using field-theoretic methods within the context of the replica scheme. In the absence of vortices we show that the model is renormalizable in a double expansion in a temperature difference variable δ and in g₀²: the strength of the disorder. The spin—spin and spin—glass correlation functions are calculated and their behavior under the renormalization group is analyzed. The spin—glass correlation function exhibits power-law behavior at any temperature but the power law is gaussian at high temperatures and controlled by a non-zero field fixed line at low temperature. Although our results agree substantially with previous work we can now point out situations in which the expansion breaks down and higher order terms must be retained. Adding vortices we can show that for $\text{p > 2}\text{2}\text{an}\text{XY}$ phase exists at intermediate values of temperature and for small values of g₀² for which our expansion is valid, vortices are irrelevant perturbations. However, in the low-temperature phase our expansion breaks down and we can no longer conclude that vortices are irrelevant. The nature of the low-temperature phase remains unresolved.     

Negative parity states and ground state properties of theα—α—n system calculated by different forces

In recent years predictions on the off-shell behavior of composite particles interactions have been made by some theoretical models. The goal of this paper is to test them by using⁹Be nucleus. The bound state problem of⁹Be considered as aα—α—n three-cluster system is solved in configuration space. Several on-shell equivalent local and nonlocal forces for theα—α andn—α interactions are used for calculation of the low lying negative parity spectrum of⁹Be, and also of the charge density, quadrupole moment, and the correlation density of⁹Be ground state. The contributions to the calculated quantities of different partial waves of the two-body forces are examined and discussed.     

Thermal diffusivity and 3D-XY critical behavior of ferroelectric semiconductors (PbxSn1−x)2P2Se6

An ac photopyroelectric calorimeter has been used to study the thermal diffusivity of the ferroelectric semiconductors family (Pb_xSn_1−x)₂P₂Se₆ (x=0–1) from 30 K to room temperature. Phase transitions have been found for x=0, 0.05, 0.2, 0.47 but not for x=1 in the full temperature range. A continuous phase transition has been found for x=0, 0.05, 0.2 and 0.47 which corresponds to the paraelectric commensurate to incommensurate phase. It has been possible to study the critical behavior of this transition for x=0, 0.05 and the critical parameters obtained have been α=−0.019, A⁺/A⁻=1.00 and α=−0.026, A⁺/A⁻=1.03, respectively, having fitted at the same time both the low and high temperature branches of the transition as rigorous critical theory indicates; these results agree with the theoretical prediction from renormalization group theory that this kind of transition complies with the 3D-XY universality class (α_theor=−0.014, A⁺/A⁻=1.06), which has been experimentally confirmed only in a few materials. A first order incommensurate to ferroelectric phase transition has been characterized in x=0, 0.05 at lower temperature.     

Classical spin systems with long-range interactions: universal reduction of mixing

We present the numerical study of chaos in a classical model of N coupled rotators on a lattice, in dimensions d=2,3. The coupling constants decay with distance as r_ij^−α (α⩾0). The thermodynamics of the model is extensive if α/d>1 and nonextensive otherwise. For energies above a critical threshold U_c the largest Lyapunov exponent scales as N^−κ, where κ is a universal function of α/d. The function κ decreases from 1/3 to 0 when α/d increases from 0 to 1, and vanishes above 1. We conjecture that this scaling law is related to the nonextensivity of the model, through a power-law sensitivity to initial conditions (weak mixing).     

Phase transition in a linear chain of classical spins with a logarithmic nearest neighbour pair potential

We present the complete calculation of the partition function and correlation functions of a linear array of classical spins coupled by a nearest neighbour logarithmic pair potential. In the case of a ferromagnetic coupling there occurs a phase transition at T_c > 0. The critical exponents of the specific heat C and the magnetic susceptibility χ (in the absence of an external field) are shown to have the non-classical value α = 2 and classical value γ = 1 respectively. The underlying mathematical mechanism of the phase transition is the complete degeneracy of all the eigenvalues of the corresponding integral equation (Kac's mechanism). Below T_c the partition function becomes complex. For antiferromagnetic coupling the free energy is analytic in the whole temperature range and so no phase transition occurs in this case.     

Comments on “Scale-free networks without growth”

In [Y.-B. Xie, T. Zhou, B.-H. Wang, Scale-free networks without growth, Physica A 387 (2008) 1683-1688], a nongrowing scale-free network model has been introduced, which shows that the degree distribution of the model varies from the power-law form to the Poisson form as the free parameter α increases, and indicates that the growth may not be necessary for a scale-free network structure to emerge. However, the model implicitly assumes that self-loops and multiple-links are allowed in the model and counted in the degree distribution. In many real-life networks, such an assumption may not be reasonable. We showed here that the degree distribution of the emergent network does not obey a power-law form if self-loops and multiple-links are allowed in the model but not counted in the degree distribution. We also observed the same result when self-loops and multiple-links are not allowed in the model. Furthermore, we showed that the effect of self-loops and multiple-links on the degree distribution weakens as α increases and even becomes negligible when α is sufficiently large.     

Mössbauer effect of119Sn in amorphous superconducting metals

Mössbauer spectra for¹¹⁹Sn in crystalline and disordered Sn, as well as in crystalline and liquid-like amorphous Sn_1-x Cu _x (X=0.10?0.18), have been measured at 2.6 K≦T≦108 K. The Debye-Waller-Factor (DWF) obtained from the spectra is identical for the crystalline and for the disordered phase. The DWF of the amorphous phase is smaller than the DWF of the crystalline phase athigh temperatures, but it shows a stronger temperature dependence than the DWF of the crystalline phase and reaches the latter one at about 4 K. From this low-temperature result we conclude that the differences of the Eliashberg functionα ²(ω)F(ω) and of the superconducting transition temperatureT _c in these two phases cannot be related to changes in the phonon spectrumF(ω), but must result from changes of the interaction parameterα ² (ω). A comparison between DWF,α ² F, and specific heat data is performed. From the values for the isomeric shift of the Mössbauer line we can show that the hybridisation and covalency of the electronic bonds present in the crystalline and in the disordered phases are destroyed in the amorphous phase. Both, the DWF and the isomer shift demonstrate that the electronic properties of crystalline and amorphous Sn(Cu) differ appreciably. The electronic and superconducting properties of amorphous Sn(Cu) are similar to the properties of the high pressure phase of tin.     

Collective behavior of coupled nonuniform stochastic oscillators

Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the literature, with equal transition rates among the states. Here we start from the model recently introduced by Wood et al. [K. Wood, C. Van den Broeck, R. Kawai, K. Lindenberg, Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators, Phys. Rev. Lett. 96 (2006) 145701], which has a collectively synchronized phase, and parametrically modify the phase-coupled oscillators to render them (stochastically) nonuniform. We show that, depending on the nonuniformity parameter 0≤α≤1, a mean field analysis predicts the occurrence of several phase transitions. In particular, the phase with collective oscillations is stable for the complete graph only for α≤α^′<1. At α=1 the oscillators become excitable elements and the system has an absorbing state. In the excitable regime, no collective oscillations were found in the model.