Ground state spin orderings of the triangular Ising model with the nearest and next nearest neighbor interaction

Low temperature Monte Carlo results are used as an indicator of the size of the repeating unit. An energy minimization is then carried out for a number of configurations. It is proposed that, in the presence of a magnetic field, there are five spin orderings according to the relative sizes of the exchange integrals.     

Critical properties of the three-dimensional frustrated Ising model on a cubic lattice

The critical properties of the three-dimensional fully frustrated Ising model on a cubic lattice are investigated by the Monte Carlo method. The critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length), as well as the Fisher exponent η, are calculated in the framework of the finite-size scaling theory. It is demonstrated that the three-dimensional frustrated Ising model on a cubic lattice forms a new universality class of the critical behavior.     

Spin orderings of the one-dimensional Ising magnet with the nearest and next nearest neighbor interaction

A proof is given of the fact that there exist four possible spin orderings for the one-dimensional Ising magnet with nearest and next-nearest-neighbor interactions.     

A conformally invariant limit of the critical lattice Ising model

A detailed analysis of an expansion in powers of 1/N (N1) for the Hamiltonian and the transfer-matrix of the Ising chain consisting ofN sites is presented. A special attention is paid to a term proportional to 1/N closely related to the theory of free massless Majorana fermions. An effective Hamiltonian isomorphic to that in conformally invariant theory is derived. The eigenvectors of the Ising Hamiltonian are classified in the framework of conformal algebra representation theory. The momentum and the energy for these states are expressed through the central charge and conformal dimensions. A similar relation for the logarithms of the transfer-matrix eigenvalues is ascertained. These are complex-valued functions of a spectral parameter . A real part of such a function is shown to be proportional to sin , while an imaginary one - to cos. A direct geometrical interpretation of the lattice spectral parameter in the context of the conformally invariant theory for fermions inhabiting a torus is indicated. In other words, these fermions are represented as analytic anticommuting variables double (anti) periodic in a complex plane. The value of the spectral parameter coincides with an angle between these (anti) periods. A general scheme for the above expansion presumably suitable for a wide class of exactly solvable models is conjectured.     

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.

     

Gauge supersymmetric Ising model on a cubic lattice near the critical point in the free field representation

The nature of the set of free fields that represent the system at the critical point has been revealed by studying the correlation functions of the degrees of freedom of the gauge supersymmetric Ising model on the cubic lattice. The same set of free fields represents the continuous supersymmetric Abelian gauge theory. Thus, the name of the lattice system is appropriate. Comparison with the two-dimensional Ising model is given.     

Analytical properties of the anisotropic cubic Ising model

We combine an exact functional relation, the inversion relation, with conventional high-temperature expansions to explore the analytic properties of the anisotropic Ising model on both the square and simple cubic lattice. In particular, we investigate the nature of the singularities that occur in partially resummed expansions of the partition function and of the susceptibility.     

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.     

A spin-one Ising model on the Bethe lattice

We study the statistical mechanics of spin-one Ising models on the Bethe lattice assuming that the spins interact by dipolar and quadrupolar interactions. An exact calculation of the properties of the system is performed on the basis of the general formulation of Morita. An exact expression for the Curie temperature is derived and the results are found to be in agreement with those of Obokata and Oguchi who utilized a generalized Bethe approximation to a spin-one Ising system. The nature of variation of the Curie temperature with respect to the change of quadrupolar exchange is discussed for various coordination numbers and the results agree qualitatively with the earlier works. The temperature variation of both dipolar and quadrupolar moments is studied.     

An improvement of the Peierls equation by taking into account the lattice effects

An improvement of the Peierls equation has been made by including the lattice effects. By using the non-trivially gluing mechanism for the simple cubic lattice, in which atoms interact with its first and second nearest neighbours through a central force, the dislocation equation has been derived rigorously for the isotropic case. In the slowly varying approximation, the Peierls equation with the improvement by including the lattice effects has been obtained explicitly. The new equation can be used to substitute for the old one in theoretical investigations of dislocations. The major change of the predicted dislocation structure is in the core region. The width of the dislocation given by using the new equation is about three times that given by the classical Peierls--Nabarro theory for the simple cubic lattice.     

Calculation of critical properties for the anisotropic two-layer Ising model on the Kagome lattice: Cellular automata approach

The critical point (K_c) of the two-layer Ising model on the Kagome lattice has been calculated with a high precision, using the probabilistic cellular automata with the Glauber algorithm. The critical point is calculated for different values of the inter- and intra-layer couplings (K₁≠K₂≠K₃≠K_z), where K₁, K₂ and K₃ are the nearest-neighbor interactions within each layer in the 1, 2 and 3 directions, respectively, and K_z is the intralayer coupling. A general ansatz equation for the critical point is given as a function of the inter- and intra-layer interactions, ξ=K₃/K₁,σ=K₂/K₁ and ω=K_z/K₁ for the one- and two-layer Ising models on the Kagome lattice.     

Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard-sphere lattice gas

We perform Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, z_c = 1.0588 ± 0.0003. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice.     

Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point . We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.     

The theory of coherent optimized-nanostructure taking laser into account the electron-electron interaction

An analytic theory of generation of a coherent laser (laser possessing a coherent electronic subsystem) operating on an optimized nanostructure is developed taking into account the electron-electron interaction. This interaction must be included since it may lead to a violation of stringent resonance conditions of coherent lasing of unipolar lasers in view of the fact that the population in such lasers increases with the pumping current. Using the Hartree-Fock approximation, analytic solutions of the Schrödinger equation were obtained for a strong electromagnetic field with open boundary conditions. The expressions derived for polarization current and electron concentration make it possible to determine the power and frequency of generation as well as amplification profile and other characteristics. It is shown that optimal lasing is realized even when electron-electron interactions are taken into account. In this optimal mode with tuning, no population inversion is required (the populations of working levels are identical). The lasing efficiency is equal to unity; the resonance-tunneling coherent pumping is effective since reflection is zero, and the amplification profile is not broadening by the field. Multimode generation stability, good spectral characteristics, and high limiting powers can be expected.     

Study of Ising model on the rectangular-triangular lattice

The Ising model is studied on a new type of lattice which is named the rectangular-triangular lattice. The critical temperature for the ferromagnetic lattice is calculated exactly and it is shown that the antiferromagnetic lattice does not order at any temperature. Ground state properties are investigated and some features of frustration on the antiferromagnetic Ising lattice outlined.     

Calculation of energy characteristics of the metal surface taking into account the lattice relaxation effects

Within the framework of the electron-density functional theory method, a self-consistent calculation of the shift of two near-surface ionic planes in different metals has been carried out. The effect of the near-surface lattice relaxation on the surface energy of metals and on the electron work function from these metallic surfaces has been investigated. To describe the arising strong inhomogeneity of the electronic system in the near-surface region, gradient corrections have been taken into account for the kinetic and exchange-correlation energy. To calculate the effect of electron-ion interaction on the energy characteristics of the surface, the Heine-Abarenkov pseudopotential has been used.     

Modeling of the processes of laser-nanoparticle interaction taking into account temperature dependences of parameters

Absorption, electron-phonon coupling and heating of nanoparticles (NPs) under action of short laser pulses on NPs and their cooling after the end of laser action usually has nonlinear character. Nonlinear electron-phonon coupling under action of pico- and femtosecond pulses on metal NPs depends on electron and lattice parameters. Optical (absorption, scattering, extinction) and thermo-physical (coefficient of thermal conductivity, heat capacity, etc.) parameters of different materials of NPs (metals, oxides, semiconductors, etc.) and environments (water, liquids, dielectrics, etc.) depend on temperature and determine nonlinear dynamics of NPs heating and cooling. It is very important to take into account the temperature dependence of optical and thermophysical parameters of NPs and surrounding media under investigation of absorption of laser radiation, electron-phonon coupling, nanoparticle (NP) heating, heat transfer and its cooling after the end of laser pulse action. Theoretical modeling of the processes of laser-NP interaction taking into account temperature dependences of parameters of NPs and environments was carried out. Influence of temperature dependences of these parameters on values and dynamics of the processes is determined.     

Monte Carlo study of the antiferromagnetical Ising model on a centred honeycomb lattice

We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies J_A-A and J_A-B in this lattice. Our study is focused on how the ratio of J_A-B to J_A-A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, {etc} each as a function of temperature for a given ratio of J_A-B to J_A-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio J_A-B / J_A-A. This work is helpful for studying the phase transition problem of crystals composed of compounds.     

Electromagnetic solitons in a system of quantum dots taking into account the Hubbard interaction

We consider the Maxwell equations for an electromagnetic field propagating in a solid with a three-dimensional superlattice of quantum dots linked by strong tunneling along one axis, where electrons with different spin projections are affected by the strong Coulomb repulsion at a single site. We obtain a phenomenological equation in the form of the classical 1+1-dimensional sine-Gordon equation. Electrons are considered within the framework of quantum formalism taking into account the changes in the dispersion law provided by the presence of Coulomb interactions. The phenomenological equation is solved numerically, and the influence of Coulomb repulsion and the degree of band population on the propagation of ultra-short optical pulses is analyzed.