Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions

The critical properties of the antiferromagnetic layered Ising model on a cubic lattice with regard to the nearest-neighbor and next-nearest-neighbor interactions are investigated by the Monte Carlo method using the replica algorithm. The investigations are carried out for the ratios of exchange nearest-neighbor and next-nearest-neighbor interactions r = J ₂/J ₁ in the range of 0 ≤ r ≤ 1.0. Using the finite-size scaling theory, the static critical indices of specific heat α, order parameter β, susceptibility γ, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is retained in the range of 0 ≤ r ≤ 0.4. It is established that the change in the next-nearest-neighbor interaction value in this model in the range of r > 0.8 leads to the same universality class as the three-dimensional fully frustrated Ising model on the cubic lattice.

     

Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J₁ and J₂, respectively. PTs in these models are analyzed for the ratio r = J₂/J₁ of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J₁ < 0 and J₂ < 0 exhibits a first-order PT in the range of 0 ? r < 0.2, whereas, in the interval 0.2 ? r ? 1.0, frustrations arise in the system. At the same time, for J₁ > 0 and J₂ < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ? |r| ? 1/3, the model exhibits a second-order PT.     

Influence of frustrations on the thermodynamic properties of the low-dimensional Potts model studied by computer simulation

Influence of disorder in the form of frustration on the thermodynamic behavior of a two-dimensional three-vertex Potts model has been studied by the Monte Carlo method, taking into account the nearest and next-nearest neighbors. Systems with linear sizes of L × L = N (L = 9–48) on a triangular lattice have been considered. It has been shown that in the case of J₁ > 0 and J₂ < 0 frustrations appear in the spin system within the interval of 0.5 ≤ |r| ≤ 1.0. The model undergoes a phase transition outside this region.     

Electron paramagnetic resonance linewidth in a two-dimensional Heisenberg antiferromagnet (S=1/2) with skyrmeons

Electron magnetic relaxation was studied in a two-dimensional Heisenberg antiferromagnet (S=1/2) with skyrmeons. The electron paramagnetic resonance (EPR) linewidth (Г_⊥) was calculated at temperatures T≤J (J is the nearest-neighbor interaction constant). The magnitude of Г_⊥ caused by the Dzyaloshinskii-Moriya interaction is shown to grow as r ₀/a with decreasing temperature, whereas the anisotropic symmetric interaction leads to the (r ₀/a)³ dependence, where r ₀ is the average size of a skyrmeon and a is the lattice parameter. The results obtained agree qualitatively with calculations performed on the basis of a renormalization-group (RG) analysis of the nonlinear σ model at .     

Determination of the constantg ωρπ from QCD sum rules

The ωρπ coupling constant is calculated using a modified form of sum rules for the vertex function 〈0|T(J _μ(x),J _ν(0))|π〉 accounting for the axial anomaly. The resultg _ωρπ=16 GeV^?1 is in good agreement with the estimates of the Vector Meson Dominance model. We show that the standard procedure gives forg _ωρπ a considerably smaller value compared to the experimental number.     

Ising model with competing interactions on a Cayley tree

An iterative scheme is developed for a renormalized effective nearest-neighbor couplingK _r and effective field per siteK _r for spins in therth shell of a Cayley tree with nearest neighborJ, and next nearest neighborJ′, interactions between Ising spins on the lattice. In addition to the expected paramagnetic, ferromagnetic, and antiferromagnetic phases, we find an intermediate range ofJ'/J < 0 values whereX _r, and K_r iterate to a continuous or quasicontinuous attractor in theX-K plane. In this range the local magnetization is mainly chaotic with oscillatory glasslike behavior. Embedded in the chaos, however, are regions of periodic and commensurate phases.     

Phase diagram of the two-dimensional Ising model with random competing interactions

An Ising model with ferromagnetic nearest-neighbor interactions J₁ (J₁>0) and random next-nearest-neighbor interactions [+J₂ with probability p and −J₂ with probability (1−p); J₂>0] is studied within the framework of an effective-field theory based on the differential-operator technique. The order parameters are calculated, considering finite clusters with n=1,2, and 4 spins, using the standard approximation of neglecting correlations. A phase diagram is obtained in the plane temperature versus p, for the particular case J₁=J₂, showing both superantiferromagnetic (low p) and ferromagnetic (higher values of p) orderings at low temperatures.     

Magnetic characteristics of MgFe<Subscript>2</Subscript>O<Subscript>4</Subscript> nanoparticles obtained by glycine–nitrate synthesis

The magnetic properties of magnesium–iron spinel (MgFe₂O₄) powdered nanoparticles obtained by glycine–nitrate synthesis are investigated by X-ray phase analysis and the NMR method. According to the results of X-ray phase analysis, the average size of the crystalline part of nanoparticles of the powder under investigation is 45 ± 4 nm. Magnetization J is determined using the formula J = (B/μ0)–H, where B and H are the induction and strength of the magnetic field in the sample, which are measured by the NMR method. The magnetic characteristics of MgFe₂O₄ are as follows: specific saturation magnetization J_sat = 17.52 A m²/kg, specific residual magnetization J_r = 5.73 A m2/kg, coercive force H_c = 4600 A/m, and magnetic moment P_sat = 371 × 10^–20 A m² in the magnetic saturation state and P_r = 121 × 10^–20 A m² in the residual magnetization state.     

Phase diagram of the Ising antiferromagnet with nearest-neighbor and next-nearest-neighbor interactions on a square lattice

The phase diagram of the Ising model in the presence of nearest-neighbor (J₁) and next-nearest-neighbor (J₂) interactions on a square lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in finite cluster (we have chosen N=4 spins). We have proposed a functional for the free energy (similar to Landau expansion) to obtain the phase diagram in the (T,α) space (α=J₂/J₁), where the transition line from the superantiferromagnetic (SAF) to the paramagnetic (P) phase is of first-order in the range 1/2<α<0.95 in contrast to previous study of CVM (Cluster Variational Method) that predict first-order transition for α=1.0. Our results for α=1.0 are in accordance with MC (Monte Carlo) simulations, that predict a second-order transition.     

Low-energy singlet sector in the spin-1/2 <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Heisenberg model on a square lattice

Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin-\(\frac{1}{2}\) Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J ₁ and J ₂. It is well known that a nonmagnetic phase arises in this model for 0.4 ? J ₂/J ₁ ? 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J ₂ ≈ 0.64 J ₁ from the non-magnetic phase to the Néel one. A large gap (? 0.4J ₁) is found in the singlet spectrum for J ₂ < 0.64J ₁, which excludes a gapless spin-liquid state for 0.4 ? J ₂/J ₁ ? 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J ₂ ≈ 0.55J ₁, presumably between two nonmagnetic phases.     

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

Long-Lived Quantum Vortex Knots

The dynamics of the simplest torus quantum vortex knots in a superfluid at zero temperature has been simulated with a regularized Biot–Savart law (the torus radii R₀ and r₀ for the initial vortex configuration are much larger than the width of the vortex core ). The evolution times of knots until their significant deformation have been calculated with a small step in the parameter B₀ = r₀/R₀ for different values of the parameter Λ = log(R₀/ξ). It has been found that regions of quasi-stability appear at Λ ? 3 in the range B₀ ? 0.2, which correspond to long knot lifetimes and very large traveling distances up to several hundred R₀. This result is new and quite surprising because previously it was believed that the maximum lifetime of torus knots until reconnection does not exceed several typical periods. The opening of quasi-stable “windows” at increasing Λ is due to narrowing of main parametric resonances of the dynamic system in the parameter B₀.     

Experimental study of the isomeric states101mRu,103mRu and101mTc

In natural Ruthenium isomeric states were produced by photonuclear reactions with LINAC Bremsstrahlung of 26 MeV. They were identified as: 526.6±0.7 keVT _1/2=22.5±0.5 μsec in¹⁰¹Ru 192.0±0.2 keVT _1/2=760±50 μsec in¹⁰¹Tc 210.9±0.2 keVT _1/2=1560±50 μsec in¹⁰³Ru The experimental techniques are described.     

Third and fourth order phase transitions: Exact solution for the Ising model on the Cayley tree

In this work we present the first exact solution of a system of interacting particles with phase transitions of order higher than two. The presented analytical derivation shows that the Ising model on the Cayley tree exhibits a line of third order phase transition points, between temperatures and , and a line of fourth order phase transitions between T_BP and ∞, where k_B is the Boltzmann constant, and J is the nearest-neighbor interaction parameter.     

Preparation of n-ZnO/p-Si solar cells by oxidation of zinc nanoparticles: effect of oxidation temperature on the photovoltaic properties

In this study, n-ZnO/p-Si solar cells were fabricated by spraying ZnO nanoparticles (NPs) film synthesised by dissolving of high purity zinc in hydrogen peroxide H₂O₂ followed by thermal oxidation in air on p-type silicon substrates. The oxidation was carried out at different temperatures (200–500) °C. The crystalline structure of the ZnO NPs films was investigated by X-ray diffraction which indicated wurtzite structure films along (100) plane. The morphology of the NPs was studied by atomic force microscopy and scanning electron microscopy. The result showed an average grain size of ZnO NPs in the range of (72.7–95.8) nm and the surface roughness increasing with oxidation temperature. Three peaks located at ultraviolet, violet and green emission regions were noticed in the photoluminescence spectra of ZnO NPs. From optical studies, it was shown that the direct optical band gap is found to be in the range of (3.85–3.96) eV depended on the oxidation temperature. The synthesised ZnO films have n-type conductivity, and the mobility was in the range of (7–24) cm² V^?1 s^?1. Current–voltage I–V and capacitance–voltage C–V of ZnO NPs/Si heterojunction solar cell were investigated as function of oxidation temperature. The spectral response of n-ZnO NPs/p-Si solar cell showed two peaks of response and its maximum value approaching 0.62 mA W^?1 at λ = 800 nm. Solar cell oxidized at 500 °C gave open circuit voltage V _OC of 375 mV, short circuit current density J _SC of 25 mA cm^?2, a fill factor FF of 0.72, and conversion efficiency η of 6.79 % under illumination of 100 mW cm^?2.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Periodic Striped Ground States in Ising Models with Competing Interactions

We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J_c(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J_c(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.     

High resolution Zeeman spectroscopy on the neon levels 2s 2 and 2p 4 by mode crossing at high magnetic fields

Mode crossing signals in laser intensity occur if the Zeeman splitting of one laser level equals the frequency separation between two laser modes. This kind of experiment using two optical frequencies for double resonance yields high resolution in Zeeman spectroscopy and allows very accurate determination ofg _J -values. Mode crossing dips of the 0.633μ, 1.152μ and 1.523μ transitions of the He-Ne-laser in an axial magnetic field were measured by tuning the field strength up to 0.17 Tesla. At this field strength the Zeeman splitting of the Dopplerbroadenedσ-lines corresponds to approximately 6 Gcps. The frequency separation between resonant modes was controlled by means of a scanning high resolution Fabry-Perot. The experimental results for theg _J -values areg _J =1.2211±0.002 for the Ne 2s ₂ level andg _J =1.3008±0.002 for the Ne 2p ₄ level. A pressure inducedg _J -shift of aboutΔg _J /(g _J ×p _He)=?1.6×10^?3/Torr for the 2p ₄ level has been observed. The influence of helium collisions disturbing the Zeeman splitting of the 2p ₄ state is discussed.