ANNNI Model Research Articles

Scattering properties of the triangular Ising antiferromagnet: Disorder and Lifshitz lines.

We study an anisotropic nearest-neighbor Ising antiferromagnet on the triangular lattice, using Monte-Carlo simulations and random-phase (or related) approximations. Our main interest concerns the high-temperature magnetic scattering. Exact results are available at the disorder line (Stephenson; Welberry and Galbraith). Of greater experimental significance is the Lifshitz line where (i) splitting of the scattering peaks occurs and (ii) dislocationlike defects appear in the (instantaneous) spin configurations. A good analytical fit of the Lifshitz line is given by the Bethe-Peierls approximation. These results could be relevant to other systems with disorder lines, e.g., the ANNNI model and microemulsions.

Series of branchings and accumulation points in modulated structures

Abstract The fixed point expansion method is used to investigate systematically the accumulation points (APs) of the ANNNI model phase diagram: At the boundary of a phase γ (e.g. ⟨3⟩) an infinite number of structure combination processes (branchings) occur (leading e.g. to ⟨23 n ⟩ phases). These branchings converge at an accumulation point. At the boundaries of each of the new phases (e.g. ⟨23 n ⟩) there are again branchings and APs etc. A procedure to calculate the APs of arbitrary phases generated by the structure combination process is described. Explicit results are given for structures occuring in the phase diagram between phases ⟨2⟩ and ⟨3⟩. For ⟨2 n 3⟩ phases the obtained AP temperatures are compared with values derived from an approximate formula.

Commensurate-commensurate phase transitions induced by an external magnetic field in spin Hamiltonians with continuous symmetry

Commensurate-commensurate phase transitions are known to occur in the Ising model with competing interactions (ANNNI model). We show that an analogous scenario may occur in spin Hamiltonians with continuous symmetry and competing interactions when an external magnetic field is applied. In particular we study a planar square lattice with exchange competition up to third neighbours. We consider exchange competition suitable for giving a zero-temperature-zero-field configuration characterized by a spin-spin turn angle Q=4 pi /5. In contrast with previous conclusions, based on the hypothesis that the unit magnetic cell does not change under the effect of an external magnetic field, we find discontinuous phase transitions between a distorted-helix phase (with five spins per cell) and the spin-flop phase (with two spins per cell) and between the spin-flop phase and a fan phase (with five spins per cell). This behaviour seems to be a general rule for large enough Q as confirmed by the helix with a turn angle Q=6 pi /7 in zero field.

Successive phase transitions - ferro-, ferri-and antiferro-electric smectics

Abstract To realize the ferrielectric phase + + - which is attributed to SmC*γ, the third neighbor interaction is introduced to the ANNNI model. General feature of phase diagram of this model is obtained, on the basis of which the successive phase transitions observed in ferro- and antiferro-electric sniectics are discussed.

Low-temperature behaviour of the six-state clock model with competing interactions

The phase diagram of the six-state clock model on a three-dimensional lattice, with first- and second-neighbour competing interactions along one direction, is analysed using a systematic low-temperature expansion carried to all orders where necessary. A transfer-matrix method simplifies the configurational analysis. We find that an infinite number of commensurate phases are stable near a zero-temperature multiphase point; a richer hierarchy of 'mixed' phases is found to be stable down to zero temperature than in the ANNNI model. The system corresponds to an XY model with infinite hexagonal anisotropy and may be relevant to rare-earth multilayers.

A microscopic model for a very stable incommensurate modulated mineral: mullite

A microscopic model is used to discuss the long-range ordering behaviour of the oxygen vacancies in mullite. This aluminosilicate of composition Al2(Al2+2xSi2-2x)O10-x (vacancy)x presents an extremely stable incommensurate modulated structure with a wave vector QIc(x) which depends on the composition index x. Earlier computer simulations showed that the oxygen vacancies strongly order the Al/Si tetrahedral sites in their local environment. When two vacancies approach too closely, their dressings overlap which results in a repulsive interaction. The system is mapped onto an ANNNI model with frustration and an additional constraint on composition x. The solutions of the authors model at thermal equilibrium are discussed in q-space as well as in real space in order to calculate QIc(x). Reasonable agreement is found with observations for x<0.5. At high concentrations of vacancies it is necessary to renormalize the coupling terms, which then accounts for the doubly modulated structure that occurs in mullite at x>0.5.

S=1 axial next-nearest neighbour Ising (ANNNI) model with higher order spin interaction

The three-dimensional S=1 axial next-nearest neighbour Ising (ANNNI) model is discussed. In addition to the ferromagnetic intra- and inter-layer interactions J0 and J1, two types of competing antiferromagnetic interactions are considered between next-nearest layers, i.e. the ordinary two-site two-spin interaction, J2SiS1+2, ((2-2) model) or three-site four-spin interaction, J3SiSi+12Si+2, ((3-4) model). For both models, the ground state is rigorously obtained by means of the transfer matrix method, and proved to change from ferromagnetic to antiphase spin structure at J2 (or J3)/J1=-1/2 with the increase of competition. From magnetization, internal energy, specific heat and 'absolute magnetization' calculated by the Monte Carlo simulation with Fourier transformation, phase boundaries among paramagnetic, ferromagnetic and modulated phases are determined with the location of the Lifshitz point. It is confirmed that for the (3-4) model the self-spin correlation, Si+12, included in three-site four-spin interaction weakens the frustration between J1 and J3 at high temperatures. In the vicinity of the paramagnetic phase transition, the correlation along the z-direction becomes considerably weaker than the correlation in xy-plane owing to the frustration along the z-direction. Consequently, for both (2-2) and (3-4) model there exists the temperature region in which the system behaves as quasi two-dimensional system.

Incommensurate structure in the lattice-gas ANNNI model

The phase diagram of the two-dimensional lattice-gas ANNNI model is investigated using the cluster transfer-matrix method. The numerical calculations have shown commensurate, disordered, and floating incommensurate phases. The properties of the incommensurate phase are studied in detail and the position of the Lifshitz point is discussed.

Comment on “Absence of PartiallyDisordered States in the AxialNext Nearest-Neighbor Ising(ANNNI) Model”

Comment on “Absence of PartiallyDisordered States in the AxialNext Nearest-Neighbor Ising(ANNNI) Model”

Polytypism in MX2 Compounds: A Case of Mixed Equilibrium Phases

AbstractClassical polytypism in MX2‐type compounds has been investigated. It has been established that polytypism can be understood, not as the case of independent stacking of A, B, or C layers but in terms of basic structural units, the most stable and only equilibrium phases of the given compounds. Other polytypes are formed only as a result of various equivalent positions that these units can take a given cell height. A criterion to predict whether a given compound would exhibit polytypism is also suggested. Several problems in applying ANNNI and other spin models to polytypism have been pointed out and a modified Hamiltonian is suggested.

Numerical Calculation of Ordered and Modulated Phases of Two-Dimensional ANNNI Model

A two-dimensional ANNNI model is investigated by an approximation method by Morita, which will be called the Scanning Line Method. Numerical calculation is performed by using a set of recurrence equations for effective fields and interactions. The modulated phase obtained is a genuine incommensurate phase and is characterized by a single wave number and its higher harmonics. Our numerical results are compared with those in earlier papers.

A model of polymorphic transformations in densely packed structures at arbitrary temperatures

An approach is described which expands the concept of the ANNNI model, within which a mathematically correct description of polymorphic transformations under load at finite temperatures is possible. The unique feature of the approach is its consideration of all possible configurations in the final block of densely packed planes for arbitrary interplane interaction. The proposed method has a number of advantages over traditional ones. The technique is illustrated by calculations of isothermal transitions 2H-3C and 9R-3C under load.

FRUSTRATED TRANSVERSE ISING MODELS: A CLASS OF FRUSTRATED QUANTUM SYSTEMS

The analytical and numerical (Monte Carlo and exact diagonalisation) estimates of phase diagrams of frustrated Ising models in transverse fields are discussed here. Specifically we discuss the Sherrington–Kirkpatrick model in transverse field and the Axial Next-Nearest Neighbour Ising (ANNNI) model in transverse field. The effects of quantum fluctuations (induced by the transverse field) on the ground and excited states of such systems with competing interactions (frustration) are also discussed. The results are compared to those available for other frustrated quantum systems.

Magnetic phase diagram and magnetic structures of Ce 4Bi 3

The ( H,T) magnetic phase diagram of Ce 4Bi 3 (cubic, a = 9.672 A ̊ space group 1 4 3d) ahs been betermined from neutron diffraction and specific heat measurements. There exist two magnetically ordered phases at low temperature. The phase II, incommensurate, is characterized by a single-k wavevector, k = 〈0, 0, 0.506〉, and has a domain of existence between 4.4 and 3.3 K ( H = 0), for magnetic fields lower than 0.2 T. The phase III, non-collinear ferromagnetic, with k = 0, develops at temperatures lower than 3.3 K ( H = 0), and the transition temperature strongly increases with the applied field. A group theory analysis based on the symmetries of the crystal and the Landau theory of phase transition allowed to determine the possible couplings between the magnetic moments of the 8 Ce atoms per unit cell. Both structures consist of noncollinear ferromagnetic layers of Ce atoms, with the moments lying along the 〈111〉 local axes, slightly tilted of 12–14° towards the common [001] axis. The incommensurate-commensurate transition towards a ferromagnetic state is foreseeable from the ANNNI model.

Commensurate configurations in the ground state of a phi 4 model with next-nearest-neighbour interactions

The ground state of an extended phi 4 Hamiltonian model including next-nearest-neighbour interactions in one direction is analysed on the basis of low coupling series expansions and numerical results. It is proven that the ground state shows commensurate configurations whose wavenumbers depend on the values of the coupling constants. The model presents a ground state diagram very similar to the phase diagram obtained in the standard 3D Ising ANNNI model for T>0.

Phase diagram of the ANNNI model in the Hamiltonian limit

The Hamiltonian limit of the ANNNI model in (1+1) dimensions is studied by using the Quantum Statistical Monte Carlo method. Even if recent results suggest that Monte Carlo calculations may prove unreliable in the study of this system, the phase diagram of the quantum version of the model was successfully obtained. In particular, the clusive transitions between the disordered, the floating incommensurate and the degenerate 〈2, 2〉 are determined by analysing the correlation length behaviour in finite lattices.

The magnetic phase transitions in Ce-monopnictides, strong p-f mixing effect

Specific heat of CeBi and CeSb, as well as LaBi and LaSb, was measured from 1.7 to 60 K under magnetic fields of up to 10 T. A Kondo like peak persists in CeBi in whole the studied region. In CeSb the effect of magnetic order is more significant but the similar situation exists, even though crossover from the Γ 7 dominated to Γ 8 dominated Kondo states appears. The γ-value is about 20 mJ/mol K 2 in both materials with weak field dependence. Phonon softening effect was also observed. It was shown that the extended ANNNI model including non-linear interactions can explain the essential feature of the complicated phase diagram in CeSb fairly satisfactorily.

Ab initio study of the Cu [sbnd]Pd one-dimensional long period superstructure phase diagram

The f.c.c. superstructure phase diagram for Cu Pd is calculated by means of isotropic effective interactions derived from an ab initio KKR-CPA electronic structure calculation. We prove the existence of a region in which one-dimensional long period superstructures are stable. This region is composed of several single phase fields in which the modulation period is constant and in close agreement with results from High Resolution Electron Microscopy. The change from wavy antiphase boundaries at low Pd concentration to sharp antiphase boundaries at high Pd concentration is related to a significant change of the interactions with Pd concentration. The role of the Fermi surface and the applicability of the ANNNI model are clarified.

Transient dynamical behavior and phase transitions in magnetic systems

It was recently suggested that transient dynamical properties were of some use to predict equilibrium critical properties of 2D and 3D models of statistical mechanics on the lattice. We investigate such dynamical properties for three related models with competitive interactions, namely the ANNNI model, the brickwork model, and the BNNNI model. In spite of known differences in their equilibrium phase diagrams, our simulations display similar transient dynamical behaviors for all three models. The reliability of this method for probing equilibrium properties seems therefore questionable even for rather simple magnetic models without any structural disorder.

Nonlinear Effect on the Axial Next-Nearest Neighbor Ising (ANNNI) Model. II. Application to CeBi

Nonlinear terms with respect to the magnetization are added to the free energy of the axial next-nearest neighbor Ising (ANNNI) model. Mean field calculations are made to investigate the phase diagram for both zero and nonzero magnetic fields. It is found that the nonlinear terms give a temperature dependent modification to the coupling constants of the conventional ANNNI model; this effect brings about a new phase transition. The nonlinear effect on the transition line between the ferromagnetic and modulated states under magnetic fields is also studied. A comparison is made between the theory and the phase diagram of CeBi in this context.