NNN Interactions Research Articles

Phase diagram of coadsorbate systems on the square lattice net

We calculate a temperature versus coverage phase diagram of a coadsorbate system on the square lattice net with nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions. In the calculation, we use the pair approximation of the cluster variation method (CVM). It is shown that in the case of repulsive nn and attractive nnn interactions, there exist three stable phases, namely the disordered phase, high-temperature ordered phase and low-temperature ordered phase, depending on temperature and coverages. The features of the phase diagram calculated for the present model are discussed.

Phase diagram of coadsorbate systems on the square lattice net

Abstract We calculate a temperature versus coverage phase diagram of a coadsorbate system on the square lattice net with nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions. In the calculation, we use the pair approximation of the cluster variation method (CVM). It is shown that in the case of repulsive nn and attractive nnn interactions, there exist three stable phases, namely the disordered phase, high-temperature ordered phase and low-temperature ordered phase, depending on temperature and coverages. The features of the phase diagram calculated for the present model are discussed.

Exact results for the spherical model with competing interactions on the Bethe lattice.

We extend to next-nearest-neighbor (NNN) interactions a technique which allows the exact solution of the spherical model of Berlin and Kac on a general discrete geometrical structure (a graph). We give the solution when the graph is a Bethe lattice. The model shows collinear (ferromagnetic or antiferromagnetic) long-range order at low temperature when NNN interactions favor the same order as nearest-neighbor ones, while it is disordered at any finite temperature when competition exceeds a critical value. For vanishing nearest-neighbor interaction the lattice decouples in two independent Cayley cacti; if the exchange on each sublattice is ferromagnetic, the model becomes ordered at a nonzero temperature, while antiferromagnetic exchange gives again disorder at any temperature.

Critical behaviour of a model with NNN interaction

A one-dimensional quantum model with next-nearest-neighbour interaction is studied. Under the long-wavelength approximation, the authors predict that this model belongs to the same universality class as the Ising model. This conclusion is checked with a numerical solution which is consistent with the prediction in both critical point and critical exponent.

On the sticking coefficient of large molecules on (100) surfaces of cubic metals

The sticking coefficient of molecules requiring several adsorption sites is calculated for various sizes and shapes of model molecules. The calculation is based on the assumption of a rigid simple quadratic lattice of adsorption sites such as the four-fold hollow sites of the (100) faces of cubic metals. The surface is considered as containing a fraction (1 − c s) of inactive sites capable of nearest- and next-nearest-neighbor interactions of which the nnn interaction is always repulsive whereas the nnn interaction may vary in sign and magnitude. The model thus describes (a) the dependence of the sticking coefficient of molecules (dissociating on adsorption) on the coverage and (b) the dependence of the initial sticking coefficient of large molecules on a pre-coverage of the surface with poisoning atoms.

A TRANSVERSE XY MODEL WITH NEXT NEAREST NEIGHBOUR INTERACTIONS

We generalize the transverse XY model to the case with NNN interactions. The Hamiltonian is H=g∑nσn2-∑n ((1+γ)/2σnxσn+1x+(1-γ)/2σnyσn+1y)-λ∑n ((1+β)/2σnxσn+2x+(1-β)/2σnyσn+2y). It is shown that the model with β=0 and γ≠0 isequivalent to the free fermion field in the vicinity of critical point, so that it belongs to the Ising universality class.

Validity of the mode-coupling theory for critical spin fluctuations in europium oxide

In order to find the range of validity of the mode-coupling theory we have solved the complete integro-differential equation for a face centered cubic lattice with nn and nnn interactions to model EuO. The recent neutron spin echo and conventional neutron scattering experiments are discussed.

Tricritical point in dilute Ising antiferromagnets in magnetic field

We show by Monte Carlo simulation that the inclusion of next-nearest-neighbor (nnn) interactions, which are always present in real systems, results in the existence of a tricritical point in the temperature-field plane. The location of this point depends on the dilution concentration p and on the nnn interaction strength. These results are discussed.

Multicritical properties of uniaxial Heisenberg antiferromagnets.

The phase diagrams of spin-1 Heisenberg antiferromagnets with ferromagnetic next-nearest-neighbor (NNN) interactions, single-site uniaxial anisotropy, and a magnetic field along the easy axis are studied. If we treat uniaxial anisotropy exactly and exchange interactions in the mean-field approximation, novel multicritical behavior is obtained at the coexistence of paramagnetic, spin-flop, and antiferromagnetic phases. New higher-order critical points are found which combine bicritical, tricritical, critical-end-point, and triple-point properties. Occurring at well-defined values of anisotropy and NNN interactions, the multicritical points merge at a new multicritical point in the four-dimensional parameter space of temperature, magnetic field, NNN interactions, and anisotropy. Appropriate phase diagrams as well as topology of the various multicritical points involved are discussed.

XY-Nature of the Fully Frustrated Ising Model on the Triangular Lattice

The XY-nature of the Ising model on the triangular lattice with the antiferromagnetic nn and ferromagnetic nnn interactions is studied by Monte Carlo simulations. The order parameter is defined via the cell spin which represents a set of Ising variables in each frustrated unit cell. The finite size effects on the x y - and z -components of the order parameter are analyzed separately. The fluctuation of the absolute value of the order parameters is introduced as a generalized susceptibility. The successive phase transition feature with the Kosterlitz-Thouless-like phase is strongly confirmed. A non-universal character of the model is discussed.

The complete two-magnon spectrum of the ferromagnetic Heisenberg chain including NNN interactions

A study of two-magnon bound states in the next-nearest-neighbour (NNN) ferromagnetic Heisenberg chain begun by Majumdar in 1969 is extended by finding the bound states and continuum resonances for all pair wave-vectors for eta =J2/J1 in the ferromagnetic range of eta =-1/4 to infinity. An exact Green function formalism is combined with the exact analytic results recently obtained by the authors for the lattice Green functions of the system to afford a definitive analysis. The Heisenberg case exhibits a modified nearest-neighbour (NN) type bound state throughout the range of eta studied and for total pair wave-vector (K=k1+k2) throughout the zone, in contrast to Majumdar who concluded that this was only the case for positive eta . The continuum also possesses a rich structure which is displayed via a shaded (grey-level) intensity plot in the ( omega , K) plane. An unexpected result is the presence of a second (anti-)bound state just above the continuum for negative eta . The evolution of the bound state and resonance structure is also examined for the transition to dominant NNN interactions. A general formulation is given which includes Ising and uniaxial anisotropies as well as biquadratic exchange for arbitrary range, dimension and Bravais lattice.

Mean Field Analysis for Successive Phase Transitions of Heisenberg-Ising Antiferromagnets on the Triangular Lattices

Phase transitions in Heisenberg-Ising antiferromagnets with nearest neighbour ( nn ) and next nearest neighbour ( nnn ) interactions on the triangular or on the hexagonal lattice are investigated by a mean field approximation. Four phases are found, namely the paramagnetic phase and three relevant types of ordered phases; (i) partially disordered phase where z -component is ordered on sublattices but the uniform susceptibility is finite, (ii) ferrimagnetic phase where the spontaneous magnetization appears and (iii) non-collinear ferrimagnetic phase where x y -components are also ordered.

Suppressed Frustration Models and Related Models in Two Dimensions

Three kinds of models with finite ground states are studied: a) A triangular Ising frustration model in which frustration is suppressed by nnn interactions, b) a triangular XY frustration model in which discrete degeneracy occurs, and c) an antiferromagnetic 3-state Potts model on a square lattice in which degeneracy is reduced by nnn interations. A description by block spins via a continuous spin transformation reduces them to a generalized 6-state clock model with cos (θ i -θ j ) and cos 3(θ i -θ j ) forms of interactions for a) and to a coupled system of Ising and XY spins for b). Model c) becomes similar to model a). Simple analyses of these equivalent models give the critical temperatures of both transitions into a Kosterlitz-Thouless phase and a longe range order, which are quite consistent with those by computer experiments. Simplified models for a) and c) are also studied and an anisotropic case is considered for a).

Exchange mechanism in europium compounds

The magnetic interaction in EuO, EuS, and EuSe is characterized by a ferromagnetic nearestneighbor (NN) interaction and an antiferromagnetic next-nearest-neighbor (NNN) interaction. While the ferromagnetic interaction decreases in strength across the series, the antiferromagnetic interaction increases in magnitude. We show that the basic mechanism for this interaction is the indirect exchange mediated by electrons occupying the anion valence bands. The band structure for these materials is first calculated by the linear combination of atomic orbitals method and then used in a perturbative calculation of the indirect exchange interaction between europium ions. The calculated results agree with the experimental values of the NN and the NNN interaction both in sign and in order of magnitude for all three compounds considered.

Statistical mechanics of equilibrium crystal shapes: Interfacial phase diagrams and phase transitions

We review the present status of the statistical mechanical theory of equilibrium crystal shapes. Special emphasis is placed on the relation between singularities occurring in the shapes of three-dimensional ( d3) crystals and the phase transitions of certain d2 models. We exploit the thermodynamic conjugacy of the Wulff plot and the equilibrium crystal shape to give interfacial phase diagrams in both density and field variables. From this perspective, sharp edges or points on the crystal shape correspond to first-order phase transitions, while smooth joining of curved and planar (“faceted”) regions corresponds to second-order phase transitions. Equilibrium crystal shapes of a simple-cubic (Ising) lattice gas with nearest-neighbor (attractive) and next-nearest-neighbor (nnn) interactions are considered in detail. Typical equilibrium crystal shapes at nonzero temperature consist of facets and smoothly curved surfaces. When nnn interactions are attractive, only second-order transitions occur. Both Kosterlitz-Thouless (“roughening”) and Pokrovsky-Talapov (Gruber-Mullins) universality classes are represented. When nnn interactions are repulsive, first-order transitions and tricritical behavior also occur. The present experimental situation is summarized.

Magnetic interaction in europium chalcogenides

The magnetic interaction in EuO, EuS and EuSe is characterized by a ferromagnetic nn interaction and an antiferromagnetic nnn interaction. We propose a mechanism for this interaction; it is an indirect exchange mediated by electrons occupying chalcogen valence bands. The LCAO energy bands are used in a perturbative calculation of the indirect exchange between two Eu ions. The calculated results agree with experiments both in sign and in magnitude for all three compounds considered.

Monte Carlo Simulation of the Antiferromagnetic Ising Model on the Triangular Lattice with the First and Second Neighbour Interactions

Monte Carlo simulations of the Ising model on the triangular lattice with the antiferromagnetic nn interaction J and the ferromagnetic nnn interaction J ' are carried out. Several physical quantities (magnetizations, energies, susceptibilities, specific heats of sublattices and of the total system) are calculated. A phase which resembles the partially disordered phase proposed by Mekata is observed in the finite temperature region. But it is shown in this region that the sublattice magnetizations vanish at the thermodynamic limit and the Kosterlitz-Thouless phase transition is predicted by the finite size analysis.

Magnetic Phase Diagram for the Triangular Ising Lattice with Antiferromagnetic Nearest-Neighbor and Ferromagnetic Next-Nearest-Neighbor Interactions

The cluster variation method is applied to calculate a temperature versus magnetic field phase diagram for the triangular Ising lattice with antiferromagnetic nearest-neighbor (nn) and ferromagnetic next-nearest-neighbor (nnn) interactions. Calculations are performed within the nn equilateral triangle plus nnn equilateral triangle approximation as well as within the molecular field approximation. The phase diagrams obtained within the former approximation are in good agreement with the Monte Carlo results of other authors except in the region of small magnetic field. The temperature and magnetic field dependence of sublattice magnetizations, total magnetization, specific heat, and susceptibility is calculated. A brief discussion is given in connection with experimental data on CsCoCl 3 and CsCoBr 3 .

Commensurate and incommensurate phases in a layered triangular system

Conventional renormalization-group $\ensuremath{\epsilon}$-expansion analysis is applied to the system of layered triangular Ising lattices with intraplane antiferromagnetic NN and NNN interactions and NN ferromagnetic interplane interactions. The Lifshitz point is a first-order point and suggests an ordinary triple-point phase diagram with the possibility of continuous transition regions on the paramagnetic-commensurate and paramagnetic-incommensurate boundaries.

Soluble classical spin model with competing interactions

The partition function and spin pair correlation functions have been calculated exactly for a classical linear chain model with alternate next-nearest-neighbor (nnn) interactions, in which the interaction energies between pairs of nearest (nn) and next-nearest (nnn) neighbor spins are arbitrary functions of the angles between the relevant spins. Of special interest is the cosine interaction model described by the Hamiltonian ℋ=−ΣNi=1[J1(cosϑ2i−1,2i +cosϑ2i,2i+1)+J2cosϑ2i−1,2i+1]. When the nnn interaction is antiferromagnetic (J2<0) it competes with the nn interaction J1, and there can be disorder point(s) at which nnn correlations change from monotonic to oscillatory. The ground state is ferromagnetic when the interaction ratio r≡J2/‖J1‖ ≳−1/2=rc, but is disordered for more negative values. The disorder point locus has been determined. It terminates at zero temperature at rD=−1/21/2, at which point the ground state energy is a maximum. The result that rD differs from rc is thought to be peculiar to one-dimensional models. Over a limited range of values of r there can be two disorder points. The low temperature asymptotic behavior of the partition and correlation functions is analyzed in detail. Also a novel summation formula for spherical Bessel functions is obtained.