Second-neighbour Interactions Research Articles

The phase diagram of the next-neighbour Ising model of the face-centred cubic lattice

We use Monte Carlo simulation to determine the stable structures in the second-neighbour Ising model on the face-centred cubic lattice. Those structures are for strongly antiferromagnetic second-neighbour interactions and for ferromagnetic and weakly antiferromagnetic second neighbours. We find a third stable “intermediate” antiferromagnetic phase with symmetry, and calculate the paramagnetic transition temperature for each. The transition temperature depends strongly on second-neighbour interactions which are not frustrated. We determine a sublattice structure suitable for solving this problem with mean-field theory.

Thermodynamics of ordering and mixing in plagioclase feldspars: atomistic modelling in favour of Landau theory

Plagioclase feldspars are key components of terrestrial planets and deriving their phase diagram and activity–composition relations has been the subject of many studies. Three main approaches have been used for thermodynamic modelling of the behaviour of plagioclase feldspars, and all three disagree in terms of the magnitude and relative importance of mixing energies and ordering energies. The present study uses Monte Carlo simulations based on classical atomistic modelling to provide independent constraints over ordering and mixing for anorthite and its solid solution with albite. Unsurprisingly, Al-avoidance plays a key role. The competition between first-neighbour and second-neighbour interactions is highlighted, providing simple explanations to the high degree of short-range order in macroscopically disordered plagioclase. The mixing properties obtained in this study support strong non-ideality, with negative mixing enthalpy and temperature-dependent mixing entropy. Ordering energies are consistent with studies using Landau theory. Unfortunately, the form of the Landau equations hindered parametrisation of a full thermodynamic model from albite to anorthite, even though the thermodynamic formalism remains simple. Reasons, perspectives, and implications for the phase diagram of ternary feldspars are discussed.

Electronic spectrum of Kekulé patterned graphene considering second neighbor-interactions

The effects of second-neighbor interactions in Kekulé-Y patterned graphene electronic properties are studied starting from a tight-binding Hamiltonian. Thereafter, a low-energy effective Hamiltonian is obtained by projecting the high energy bands at the Γ point into the subspace defined by the Kekulé wave vector. The spectrum of the low energy Hamiltonian is in excellent agreement with the one obtained from a numerical diagonalization of the full tight-binding Hamiltonian. The main effect of the second-neighbour interaction is that a set of bands gains an effective mass and a shift in energy, thus lifting the degeneracy of the conduction bands at the Dirac point. This band structure is akin to a ‘pseudo spin-one Dirac cone’, a result expected for honeycomb lattices with a distinction between one third of the atoms in one sublattice. Finally, we present a study of Kekulé patterned graphene nanoribbons. This shows that the previous effects are enhanced as the width decreases. Moreover, edge states become dispersive, as expected due to second neighbors interaction, but here the Kek-Y bond texture results in an hybridization of both edge states. The present study shows the importance of second neighbors in realistic models of Kekulé patterned graphene, specially at surfaces.

Competition between supersolid phases and magnetization plateaus in the frustrated easy-axis antiferromagnet on a triangular lattice

The majority of magnetic materials possess some degree of magnetic anisotropy, either at the level of a single ion, or in the exchange interactions between different magnetic ions. Where these exchange interactions are also frustrated, the competition between them and anisotropy can stabilize a wide variety of new phases in applied magnetic field. Motivated by the hexagonal delafossite 2H-AgNiO 2, we study the Heisenberg antiferromagnet on a layered triangular lattice with competing first- and second-neighbour interactions and single-ion easy-axis anisotropy. Using a combination of classical Monte Carlo simulation, mean-field analysis, and Landau theory, we establish the magnetic phase diagram of this model as a function of temperature and magnetic field for a fixed ratio of exchange interactions, but with values of easy-axis anisotropy D extending from the Heisenberg (D =0) to the Ising (D=&#8734) limits. We uncover a rich variety of different magnetic phases. These include several phases which are magnetic supersolids (in the sense of Matsuda and Tstuneto or Liu and Fisher), one of which may already have been observed in AgNiO 2. We explore how this particular supersolid arises through the closing of a gap in the spin-wave spectrum, and how it competes with rival collinear phases as the easy-axis anisotropy is increased. The finite temperature properties of this phase are found to be different from those of any previously studied magnetic supersolid.

Flexible magnetoinductive ring MRI detector: Design for invariant nearest-neighbour coupling

A flexible birdcage-type resonant RF detector for magnetic resonance imaging is described. The circuit consists of a polygonal ring of magnetically coupled L– C resonators, a periodic structure supporting backward magnetoinductive waves. The elements are mechanically linked to allow relative rotation, and the pivot point is optimised to hold the nearest-neighbour coupling coefficient invariant to small changes in the angle of an undistorted joint. Simple theory based on a parallel wire approximation to rectangular inductors is developed to allow the variation of the coupling coefficient with angle and radius to be estimated, and hence determine the location of the pivot. The optimised pivot is shown to reduce resonance splitting in octagonal rings. However, second-neighbour interactions degrade performance. The theory is verified experimentally using printed circuit board elements coupled by flexible hinges, and the invariance of the nearest-neighbour coupling coefficient is confirmed. Octagonal ring resonators are constructed for operation at 63.8 MHz frequency and the mode spectra of regular and distorted rings are measured. Magnetic resonance imaging properties are investigated using 1H MRI of simple objects in a 1.5 T field. Images are obtained from undistorted and distorted resonators and the effect of distortion on SNR is quantified.

Spin–spin correlation in some excited states of the transverse Ising model

We consider the transverse Ising model in one dimension with nearest neighbour interaction and calculate exactly the longitudinal spin–spin correlation for a class of excited states. These states are known to play an important role in the perturbative treatment of the one-dimensional transverse Ising model with frustrated second-neighbour interaction. To calculate the correlation, we follow the earlier procedure of Wu, use Szego's theorem and also use the Fisher–Hartwig conjecture. The result is that the correlation decays algebraically with distance (n) as 1/√n and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.

The ground state of an XXZ chain with asymmetric second-neighbour interactions

The ground state phase diagram of anXXZ chain with asymmetric second-neighbour interactions is studied. We first prove that thismodel has the doubly degenerate exact dimer ground state under some conditions. Then,by using the level spectroscopy method, we calculate the ground state phase diagram andfind that the dependence of the dimer–fluid critical line on the asymmetric interactions ismuch stronger than those of the dimer–Néel critical line and the ferro-fluid first-ordertransition line. In order to understand this result, we analyse eigenvectors ofthe ground state and excitations characterizing each of phases, and show thatonly the doublet excitation can be used to detect the asymmetric interactions.

Tight-binding studies of the electronic band structure of GaAlN and GaInN alloys

The semi-empirical tight-binding (TB) approach with an sp3s* orbital basis is used to investigate the electronic band structure of cubic Ga1-xAlxN and Ga1-xInxN alloys. The spin–orbit splitting in the Hamiltonian and first- and second-neighbour interactions are considered to explore the gap evolution as a function of the concentration x. The TB parameters used in the studies were obtained within the virtual crystal approximation using those of the binary compounds AlN, GaN, and InN. The binary parameters are calculated by applying an empirical TB Hamiltonian taking into account first- and second-neighbour interactions. A direct to indirect gap transition is obtained for Ga1-xAlxN at x=0.60. In contrast, the Ga1-xInxN alloys exhibit direct-gap characteristics as a consequence of being formed by the direct-gap binary compounds GaN and InN.

Tight-binding calculation of the electronic band structure of GaN, AlN and BN (0 0 1) ideal surfaces

We study the electronic band structure of the zinc-blende phase (0 0 1) ideal surface of GaN, AlN and BN by means of an empirical tight binding sp 3 s * Hamiltonian with nearest-neighbour interactions plus some second-neighbour interactions and the surface Green function matching method. We have studied both anion and cation terminated surfaces and we have obtained the different surface states with their corresponding spectral localization and orbital character.

Urotropin azelate: a rather unwilling co-crystal.

Urotropin (U) and azelaic acid (AA) form 1:1 co-crystals (UA) that give rise to a rather complex diffraction pattern, the main features of which are diffuse rods and bands in addition to the Bragg reflections. UA is characterized by solvent inclusions, parasite phases, and high vacancy and dislocation densities. These defects compounded with the pronounced tendency of U to escape from the crystal edifice lead to at least seven exotic phase transitions (many of which barely manifest themselves in a differential scanning calorimetry trace). These involve different incommensurate phases and a peritectoid reaction in the recrystallization regime (T(h) > 0.6). The system may be understood as an OD (order-disorder) structure based on a layer with layer group P(c)c2 and cell a(o) approximately 4.7, b approximately 26.1 and c approximately 14.4 A. At 338 K the layer stacking is random, but with decreasing temperature the build-up of an orthorhombic MDO (maximal degree of order) structure with cell a(1) = 2a(o), b(1) = b, c(1) = c and space group Pcc2 is begun (at approximately 301 K). The superposition structure of the OD system at T = 286 (1) K with space group Bmmb and cell â = 2a(o), b = b and ĉ = c/2 owes its cohesion to van der Waals interactions between the AA chains and to three types of hydrogen bonds of varied strength between U-U and U-AA. Before reaching completion, this MDO structure is transformed, at 282 K, into a monoclinic one with cell a(m) = -a(o) + c/4, b(m) = b, c(m) = -2(a(o) + c/2), space group P2(1)/c, spontaneous deformation approximately 2 degrees, and ferroelastic domains. This transformation is achieved in two steps: first a furtive triggering transition, which is not yet fully understood, and second an improper ferroelastic transition. At approximately 233 K, the system reaches its ground state (cell a(M) = a(m), b(M) = b, c(M) = c(m) and space group P2(1)/c) via an irreversible transition. The phase transitions below 338 K are described by a model based on the interaction of two thermally activated slip systems. The OD structure is described in terms of a three-dimensional Monte Carlo model that involves first- and second-neighbour interactions along the a axis and first-neighbour interactions along the b and c axes. This model includes random shifts of the chains along their axes and satisfactorily accounts for most features that are seen in the observed diffraction pattern.

LOW-TEMPERATURE SERIES EXPANSIONS FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.

Stationary breather modes of generalized nonlinear Klein-Gordon lattices

This paper studies the form of stationary breather modes in discrete generalized nonlinear Klein-Gordon equations, with symmetric and non-symmetric potential energy functions. In the case of static breathers, the discrete nature of the spatial dimension has a much more subtle effect on the breather than the moving breather mode. This effect is analysed using a variety of approximating partial differential equations, whose solutions are found by using an extended multiple-scales asymptotic approach to reduce the equation to a nonlinear Schrodinger equation at leading order and more complex equations at higher order, where secularity conditions are required to fully specify the solution. As well as the much studied discrete sine-Gordon equation, the methods are demonstrated on a discrete nonlinear Klein-Gordon equation with second-neighbour interactions and non-symmetric on-site potential. New partial differential equations which approximate these lattice systems are also proposed and analysed.

High-temperature series expansions of susceptibility of the square-lattice Ising model with first- and second-neighbour interactions

We have calculated exactly the high-temperature series expansions of the susceptibility of the Ising model with equal first- and second-neighbour interactions on the square lattice up to 18th order by computer. Soehianie and Oitmaa computed the same series expansions up to 13th order and their result agrees with ours. We use the Padé approximants to estimate the critical exponent γ and find that 1.745< γ<1.755. Our result is consistent with the universality hypothesis which predicts that square-lattice Ising models with interactions beyond first neighbours have the same critical exponent γ=1.75 as the square-lattice Ising model with nearest-neighbour interactions.

The Low-Temperature Three-Dimensional Structures of the Second-Stage Caesium Graphitide

The three-dimensional (3D) structure of the second-stage CSC24 graphitide was investigated by recording hk.l monochromatic rotating-crystal diffractograms. At low temperature, the two-dimensional (2D) structure is formed of an incommensurate (2.53 x 2.53 R 14.5°) and a commensurate (2 x 2 R 0°) lattice. Below 140 K, whereas the Cs incommensurate layers become 3D ordered, the 2 x 2 R 0° commensurate layers are randomly distributed in the structure. The commensurate structure, with composition CsC16 (stage two), probably equilibrates the lack of Cs induced by the incommensurate structure (composition CSC26), in order to reach the global composition CSC24 of the compound. Depending on the temperature, two kinds of stackings appear. Below 140 K, the incommensurate Cs layers are arranged in a 2D-modulated initial stacking, transformed at a lower temperature into a rhombohedral stacking in which Cs atoms are modulated along the c axis. Simulation of the selection rules allowed the determination of models of the incommensurate layers stacking along the c axis, with translations from one Cs layer to another layer commensurate with the graphite lattice. The initial stacking is described by a pseudo-two-layer model with successive random translations and a short-range order. The structure appearing at a lower temperature is described by a pseudorhombohedral stacking with definite translations. The transition from the initial stacking with a first-neighbour interaction to the pseudorhombohedral stacking with a second-neighbour interaction could be a result of the change in interactions between the Cs atoms and the graphitic host, due to the dominating influence of the graphite periodic potential at low temperature.

Approximations to solitary waves on lattices, III: the monatomic lattice with second-neighbour interactions

We find new behaviour in a lattice with second-neighbour interactions. First we find solitary waves with oscillatory spatial decay, this is something that cannot occur in lattices with nearest-neighbour interactions alone. This is found by standard asymptotic analysis, which leads to an exact curve in parameter space where this behaviour starts. A number of highly accurate quasi-continuum approximations are derived and solved. One of these suggests a possible method for subsonic solitary waves to cease existing. An alternative method of approximation elegantly reveals the differences in shape between subsonic and supersonic solitary waves. This is based on the weak form of the differential - delay equation for the travelling wave, and is derived using the calculus of variations.

Tricritical behaviour of the ferromagnetic Blume-Capel model with first- and second-neighbour interactions

A ferromagnetic Blume-Capel model with first- and second-neighbour interactions is investigated by the use of the effective-field theory with correlations. The general expressions for evaluating the second-order phase transition and the tricritical point are obtained. Particular emphasis is given to the square lattice for which the dependence of the position of the tricritical point on the relative strengths of the second- and first-neighbour interactions is investigated.

GAMMEL: A program for the calculation of the pressure dependence of the elastic constants of ionic crystals

Program GAMMEL has been developed for the calculation of different elastic properties of ionic solids, in particular their pressure dependence. Sodium chloride, caesium chloride and the fluorite structures were studied; an analysis of central and non-central forces was allowed for, considering up to second-neighbour interactions using different potential forms and parametrizations. The program has a flexible structure and allows for a check with experimental elastic data and a cross-checking with an anharmonic property (thermal expansion in the limit of low temperatures).

Phase transitions in Ising square antiferromagnets with first- and second-neighbour interactions

The phase transitions occurring in the Ising square antiferromagnet with first- (J1) and second- (J2) nearest-neighbour interactions are studied using several mean-field approximations and for a wide range of R=J2/J1. The largest approximation used corresponds to a nine-point cluster approximation of the cluster variation method. In this case, the transition temperatures as a function of R are found to be in excellent agreement with those obtained by other methods. The mean-field approximations predict a first-order transition in the range 0.5<R<or approximately=1.2, where the critical exponents associated with the paramagnetic to superantiferromagnetic transition have been reported to vary continuously with R. In that range of R, the mean-field approximations also predict a crossover between two distinct instability temperatures, or spinodals, taking place immediately below the first-order transition. Mean-field results are also given for the magnetization m, the specific heat Cnu , the magnetic susceptibility X, the staggered susceptibility Xs, and the pair correlation function sigma ij between i and j sites.

Random-field Ising model with second-neighbour interaction

A random-field Ising model with second-neighbour interaction has been investigated using the new effective-field theory. The phase diagrams are examined in detail for the square lattice in a random field obeying the bimodal symmetric distribution. A tricritical point is found in the system, in contrast to the corresponding nearest-neighbour interaction Ising model. In particular, the tricritical phase diagram for a body-centered cubic lattice in nearest-neighbour approximation is also determined.

The CLE condition and the correlation length on the square lattice Ising model with first- and second-neighbour interactions

The square Ising lattice with nearest- and next-nearest-neighbour interactions is considered. On the basis of the simplest ansatz on the principal eigenvector of the transfer matrix of the model and of the CLE condition, developed in previous papers, the correlation length along a column is calculated for all T>or=Tc, in the ferromagnetic and antiferromagnetic regions. A comparison is made with results obtained through other methods. For competing interactions, it is shown that there is a mechanism which leads to a correlation length made of two analytic pieces.