Narrow Results

Some results on the two-point function and on the analytic structure of the momenta of the effective fugacity at the origin for a class of diluted ferromagnetic Ising models on the Cayley tree are presented.

The tail of the distribution for the "mean cluster size" (susceptibility) at the site percolation threshold is found by Monte Carlo simulations to be exponential. Similar distributions might be expected for the market volatility, if stock price fluctuations are described by Cont–Bouchaud percolation.

Transfer matrix calculations of the critical two-point correlation function in 2D Ising model on a finite-size lattice with periodic boundaries along 〈11〉 direction are extended to L = 21. A refined analysis of the correlation function in 〈10〉 crystallographic direction at the distance r = L indicates the existence of a nontrivial finite-size correction of a very small amplitude with correction-to-scaling exponent ω < 2 in agreement with our foregoing study for L ≤ 20. Here we provide an additional evidence and show that amplitude a of the multiplicative correction term 1 + aL^-ω is about -3.5·10^-8 if ω = 1/4 (the expected value). We calculate also the susceptibility for L ≤ 18 in order to compare our numerical estimates for the constant background contribution with the known very precise value and to look for possible nontrivial corrections to scaling. The numerical analysis reveals a perfect agreement for the background term, as well as shows that the nontrivial correction term, detected by our analysis in the correlation function, likely cancels in the susceptibility.

To determine the susceptibilities of Mycoplasma homonis (M. hominis) to Chinese medicinal herbs in vitro, 30 clinical strains of M. hominis were isolated and identified from the clinical specimen. The susceptibilities of M. hominis to 19 herbs were determined by serial dilution methods in vitro. The results showed that M. hominis was susceptible to Radix Isatidis, Radix Angelicae Dahuricae, Cortex Phellodendri, Radix et Rhizoma Rhei, Fructus Kochiae and Herba Houttuyniae. These findings laid a foundation in treating M. hominis infection with Chinese herbs.

In this paper, chiral chemical potential ${\mu }_5$ is introduced to investigate the QCD susceptibilities and chiral phase transition within the Polyakov-loop-extended Nambu–Jona-Lasinio models in the mean-field approximation. We concentrate on the effect of chiral chemical potential on the phase diagram and the QCD susceptibilities. Moreover, it is worth noting that chiral chemical potential has more and more prominent impact on the susceptibilities and the phase diagram with the decrease of temperature based on our results, which coincides with the prediction that the chiral symmetry is dynamically broken in the first-order phase transition region and gets partly restored in the crossover region.

We calculate the second-order corrections to vacuum polarization tensor of photons at low temperatures, i.e. T ≪ 10¹⁰K(T ≪ m_e). The thermal contributions to the QED coupling constant are evaluated at temperatures below the electron mass that is T < m_e. Renormalization of QED at these temperatures has explicitly been checked. The electromagnetic properties of such a thermal medium are modified. Parameters like electric permittivity and magnetic permeability of such a medium are no more constant and become functions of temperature.

The longitudinal susceptibility χ_L of the O(N) theory in the broken phase is analyzed by means of three different approaches, namely the leading contribution of the 1/N expansion, the Functional Renormalization Group flow in the Local Potential approximation and the improved effective potential via the Callan–Symanzik equations, properly extended to d = 4 dimensions through the expansion in powers of ϵ = 4-d. The findings of the three approaches are compared and their agreement in the large N limit is shown. The numerical analysis of the Functional Renormalization Group flow equations at small N supports the vanishing of in d = 3 and d = 3.5 but is not conclusive in d = 4, where we have to resort to the Callan–Smanzik approach. At finite N as well as in the limit N→∞, we find that vanishes with J as J^ϵ/2 for ϵ> 0 and as (ln(J))^-1 in d = 4.

We evaluate the second to fourth-order baryon, charge and strangeness susceptibilities near a chiral critical point using the Nambu–Jona-Lasinio model under different temperatures and baryon chemical potential. Baryon number susceptibilities are found to be of the greatest magnitude, offering the strongest signal. Whereas the strangeness susceptibilities have the smallest divergence dominating area, owing to the large strange quark mass. We also make an attempt to compare our results with experiment data. The trend at high collision energy is found to be consistent between theory and experiment. The model calculation predicts more complex behavior at low collision energies, near the postulated critical end point.

The effect of partial substitution of Ca by Eu, Sm and Er on the structural, transport and magnetic properties of (Bi_1.6Pb_0.4)Sr₂(Ca_1-xRE_x)₂Cu₃O_y superconductors ceramics (0≤x≤0.025) have been investigated. The substitution of Eu, Sm and Er at the Ca site induced the decrease of the volume fraction for the 2223 phase and the increase of 2212 and 2201 phase volume fractions. The rate of depression for the critical temperature in x=0.015 samples found to be nearly the same for all of these substitutions. The nature of T_c suppression may be attributed to the increase of oxygen content in Bi₂O₂ double layers with increasing Eu, Sm and Er concentrations. The samples shows a linear dependence of intergranular temperature as a function of AC field amplitude, which is in agreement with Muller critical state model.

The thermal behaviors of the order-parameters, susceptibility and specific heat of the mixed spin-½ and spin-1 Blume–Capel Ising ferrimagnetic system is studied on the Bethe lattice by using the exact recursion equations. The exact equations for the order parameters and the susceptibility are obtained for the sublattices with spin-1 and spin-½. Also, the exact expressions for the free energy and the specific heat are obtained on the Bethe lattice as a whole system. Then the thermal behaviors of the order-parameters, susceptibility, inverse susceptibility and specific heat are studied for the coordination numbers q=4 and q=6. The obtained results are illustrated and discussed in detail.

Ru_1-xSb_xSr₂(Eu_0.7Ce_0.3)₂Cu₂O_10-δ systems were prepared by conventional solid state reaction method. The structural analysis was investigated using X-ray diffraction. Electrical resistivity, Hall effect and magnetic susceptibility measurements on Ru:1222 doped with Sb are presented, together with results in the temperature range 5–300 K. Transition temperature decreases from 43 K for x = 0.00 to 20 K for x = 0.06 Sb. This may be due to a distortion of RuO₆ octahedral, which is responsible of the increase in hole localization. The Hall effect anomalous decreases below T_magnetic which may be explained within a simple two-band model by a transition from localized to more itinerant behavior in the RuO₂ layer at T_magnetic. The behavior of magnetic susceptibility is caused by an antisymmetric exchange coupling of the Dzyaloshinsky–Morya type between neighboring Ru moments.

A series of composite ferrites with chemical formula (1–x)[Mn_0.5Zn_0.5Fe₂O₄]·x[SiO₂](x = 0.0, 0.20, 0.30, 0.40, 0.50) were prepared by the co-precipitation technique. The samples were finally sintered at 1150°C followed by air quenching. The x-ray diffraction analysis confirms the phases precipitated out in the samples. AC magnetic susceptibility of these samples has been measured using the low field mutual inductance technique over the temperature range 298 K to 550 K at a frequency of 250 Hz. The magnetic parameters like Curie constant, C, Curie temperature, T_c, Lande splitting factor, g, effective magnetic moment, P_eff, exchange integral, J/kB, and characteristic temperature, θ(K) were calculated. The reciprocal of susceptibility versus temperature curves of each sample follows the Curie Weiss behaviour above the Curie temperature. Below the Curie temperature, all the samples show the ferrimagnetic behaviour. It was concluded that the magnetic properties were enhanced by the addition of silicon as is evident by the variation of magnetic interactions J, with Si-concentration and followed subsequently by the P_eff, θ(K) and T_c etc.

We study the mesoscopic orbital magnetism of a free electron gas in a rectangular box in the zero-temperature limit. We find that, as in weakly disordered systems, it can be well-described by the van Vleck susceptibility that couples just two size-quantized energy levels: the Fermi (last occupied) level and the first unoccupied level. Large fluctuations of the off-diagonal matrix elements of the angular momentum and, more importantly, of the nearest level spacings — level bunching characteristic of classically integrable systems — are responsible for the absence of effective self-averaging in this system. We develop a detailed analytical description and conduct extensive numerical simulations based on a combined averaging over the energy spectrum, and over the aspect ratio of rectangles with equal areas.

The statistical weight W as a function of energy E for quasielectrons with mass m* subject to a fixed magnetic field B is , where A is the sample area, and ω_c ≡ eB/m* the cyclotron frequency. Significantly, there is no Landau term proportional to B² in 2D. This leads to the conclusion that the 2D electron system is always paramagnetic, but shows a magnetic oscillation.

The thermodynamics of a superconductor, with pairing and quartet-binding BCS-type attractions V_BCS and V, is investigated in the strong-coupling limit. The coupled equations for the gap parameters Δ_G, Δ_g, corresponding to both potentials, are solved and the thermodynamic functions are computed for varying coupling constant g₀ of the quartet attraction V. Some untypical thermal properties of tin, mercury, and high-T_c superconductors, which have not been fully explained by theory, are found to agree with this strong-coupling thermodynamics. Sufficiently strong V eliminates the BCS pairing potential and the conducting fermions behave as if they were interacting only via V. The structure of the condensate at T = 0 is studied and shown to consist almost exclusively of Cooper pairs if g₀ ≤ 0.2G₀ (G₀ denoting the coupling constant of V_BCS), whereas if g₀ > 2G₀, all fermions merge into quartets.

In this paper, the Monte Carlo simulation (MCS) and the mean field approximation (MFA) methods have been used to study the magnetic properties of double perovskite Ba₂CrMoO₆ in the framework of the Ising model, which is important for a better understanding of the magnetic behavior of this material. This compound is constituted of two magnetic cubic sublattices: one occupied by Mo${}^{5+}$ and other occupied Cr${}^{3+}$, the critical exponents and phase diagrams for this compound are determined. The critical behavior, compensation temperature and susceptibility are also determined.

An analytic technique for calculating the correlation function and correlation radius of systems belonging to the universality class of the three-dimensional Ising model is elaborated within the collective variables (CV) method. The calculations of these nonuniversal characteristics are performed for the temperatures $T>T_{\mathrm{\text{c}}}$, $T<T_{\mathrm{\text{c}}}$ and $T=T_{\mathrm{\text{c}}}$ ($T_{\mathrm{\text{c}}}$ is the phase transition temperature) on the microscopic level in the approximation of the quartic distribution for modes of spin moment density oscillations (the ${\rho }^4$ model). Proceeding from the expression for the Fourier transform of the correlation function, we have also obtained the susceptibility of the system. The correction to scaling and the potential averaging correction are taken into account in our calculations.

Tilt angle (order parameter) and the susceptibility are calculated as a function of temperature for the $\alpha$–$\beta$ transition in quartz using a Landau phenomenological model. The tilt angle as obtained from the model is fitted to the experimental data from the literature and the temperature dependence of the tilt angle susceptibility is predicted close to the $\alpha$–$\beta$ transition in quartz. Our results show that the mean field model explains the observed behavior of the $\alpha$–$\beta$ phase transition in quartz adequately and it can be applied to some related materials.

Nowadays, it happens very often that in order to make a decision we rely on knowledge originating from different and autonomous sources, i.e. from experts or the Internet. For many problems we often ask for an opinion of not one but a group of sources (a collective). It may be due to the fact that we collect very large amount of information which might be inconsistent unfortunately. The process of appointing the knowledge state of a collective (final and consistent opinions) is often very complex and time-consuming. Therefore, we want to know if it is possible to determine a common and reliable opinion of a collective only by analyzing given knowledge of a collective. For this task the consensus theory is applied. This work is devoted to analyses of a susceptibility to a consensus for a few types of representations of experts' opinions (knowledge of a collective) such as a number, a binary vector, ordered partitions or ordered coverings.

A developed effective chiral Lagrangian approach is used to study the cold dense nuclear matter. Improved calculation of baryon number density as a function of chemical potential is given. The resonance appeared in a natural way as chemical potential is getting larger. Calculations of susceptibility and pressure including the resonance contribution are also given.