Quantum spin model of a cubic ferromagnet in a magnetic field

The zero temperature phase diagram of a one-dimensional ferromagnet with cubic single ion anisotropy in an external magnetic field is studied. The mean-field approximation and the density-matrix renormalization group method are applied. Two phases at finite magnetic fields are identified: a canted phase with spontaneously broken symmetry and a phase with magnetization along the magnetic field. Both methods predict that the canted phase exists even for the single-ion anisotropy strong enough to destroy the magnetic order at zero magnetic field. In contrast to the mean-field theory, the density-matrix renormalization group predicts a reentrant behavior for the model. The character of the phase transition at finite magnetic field has also been considered and the critical index has been found. Received 9 May 2000 and Received in final form 5 July 2000     

Purely quadrupolar spin-1 Ising model in a transverse field

A quantum Ising-like spin-1 model characterized by quadrupolar interaction, coupled to an external anisotropic field with both dipole and quadrupole momenta is analyzed. The general phase diagram (including temperature), as well as order parameter, specific heat, and susceptibility are evaluated in the mean-field approximation and exibit a rich structure with transitions of 2° and 1° order and tricritical points. ForT=0 the phase diagram is examined also by a recently formulated improved version of mean-field theory which has the usual mean-field theory as its zero-th order approximation.     

格点变模SU（2）－Higgs模型的解析计算

在四维空间对格点ＳＵ（２）－Ｈｉｇｇｓ模型的序参量Ｅｐ＝〈ｔｒＵｐ〉〉用累积展开计算到四级近似．Ｈｉｇｇｓ场为基础表示．发展了定双变分参数的办法．得到的相图与蒙特卡罗结果有好的符合．     

Lattice dynamics and phase diagram of aluminum at high temperatures

The dispersion of phonons in the fcc, hcp, and bcc phases of aluminum is calculated at ultrahigh pressures by the method of small displacements in a supercell. The stability of the phonon subsystem is studied. The thermodynamic characteristics are calculated in the quasi-harmonic approximation, and a phase diagram of aluminum is plotted. As compared to the Debye model, the use of a phonon spectrum calculated in the quasi-harmonic approximation significantly broadens the hcp phase field and strongly shifts the phase boundary between the fcc and bcc phases. The normal isentrope is calculated at megabar pressures. It is shown to intersect the fcc-hcp and hcp-bcc phase boundaries. The sound velocity along the normal isentrope is calculated. It is shown to have a nonmonotonic character.     

The influence of the short-range ferromagnetic order on the itinerant-electron antiferromagnetism

The short-range spin—spin impurities interaction in the itinerant-electron antiferromagnet is considered in a model with quenched impurities. In the mean field approximation the phase diagram is calculated.     

Quantum phase transition in spin glasses with multi-spin interactions

We examine the phase diagram of the p-interaction spin glass model in a transverse field. We consider a spherical version of the model and compare with results obtained in the Ising case. The analysis of the spherical model, with and without quantization, reveals a phase diagram very similar to that obtained in the Ising case. In particular, using the static approximation, reentrance is observed at low temperatures in both the quantum spherical and Ising models. This is an artifact of the approximation and disappears when the imaginary time dependence of the order parameter is taken into account. The resulting phase diagram is checked by accurate numerical investigation of the phase boundaries.     

Ising model with frustration,elasticity, and competing interactions

The Ising model on a compressible triangular lattice with axial next-nearestneighbor interactions is studied in the mean-field approximation. A representative phase diagram is generated, which exhibits first- and second-order phase transitions to commensurate modulated phases. The crossover point from first to second order transitions is calculated. The stability of the modulated phases is calculated analytically in a low-temperature approximation. These results are very different from the ANNNI model, which exhibits a second-order transition to a continuum of commensurate and incommensurate phases.     

Chemical short-range-order effects on stability in δ-Pu–Ga alloys

We present results on the structural stability of Pu_{1? x} Ga _x alloys based on the local spin-density approximation and including non-local corrections to the exchange–correlation functional (generalized gradient approximation). First, we used both the linearized augmented plane-wave and the projector augmented wave (PAW) methods to calculate the energies of formation of five intermediate phases which occur in the Pu–Ga phase diagram. Then, PAW calculations were performed for various superstructures based on the fcc lattice to get the interaction parameters to describe the energetics of the δ-Pu–Ga solid solution. To discuss the effects of the chemical short-range order on the structural stability of the δ-Pu–Ga solid solution as a function of temperature, the cluster variation method configurational entropy has been introduced using the regular tetrahedron approximation. The solid part of the Pu-rich side of the phase diagram involving phase equilibria between the Pu phases, the δ-Pu–Ga solid solution and the Pu₃Ga compound is calculated. We show the importance of chemical short-range order on Ga solubility in δ-Pu.     

Particle clustering and Mott transition in nuclear matter at finite temperature (II): Self-consistent ladder Hartree-Fock approximation and model calculations for cluster abundances and the phase diagram

Hot nuclear matter is described in terms of a quantum statistical approach. A self-consistent ladder Hartree-Fock approximation is derived in order to achieve a simultaneous treatment of free nucleons, douterons and higher clusters. In this approximation the effect of the correlated medium on the cluster abundances is studied. The Mott mechanism is pointed out in which clusters are destructed for densities beyond the Mott density. Cluster abundances and a phase diagram are calculated by means of a model calculation based on a simplified Skyrme interaction. The role of the higher clusters in calculating the phase diagram is investigated. The possible existence of a first-order phase transition in hot nuclear matter is discussed.     

Lattice-gas model of multiple layer adsorption

The phase diagram for a lattice-gas model of physical adsorption on a homogeneous substrate has been calculated in a mean-field approximation. The first-order phase transitions corresponding to the addition of successive layers terminate in individual critical points as the temperature increases. The critical temperatures of successive layers increase, monotonically with layer number, from the critical temperature of the two-dimensional lattice gas to that of the bulk three-dimensional lattice gas. This last feature is probably an artifact of the mean-field approximation.     

Transition from smectic-A to crystalline phase in the mean field approximation

We present here a smectic-A to crystalline phase transition curve for liquid crystals, in addition to the phase diagram previously reported which includes the isotropic, nematic, and smectic-A phases calculated in the mean field approximation.     

The bethe approximation to the three-state chiral clock model

The three-state chiral clock model is studied by means of the Bethe approximation. While the phase diagram obtained by this method resembles the mean-field phase diagram in the vicinity of the boundary to the paramagnetic phase, a significant improvement is achieved in the low and intermediate temperature regions: By a low-temperature expansion of the free energy, which is carried out to third order, we find that, up to this order, the Bethe approximation exactly reproduces the results of the low-temperature analysis of the full model by Yeomans and Fisher. This and the numerical evaluation of the free energy show that, as far as the longer wavelength phases are concerned, the Bethe approximation is in keeping with predictions of Yeomans and Fisher for low temperature, where mean-field theory is qualitatively misleading. At higher temperatures more complicated structures are found to evolve from the basic low-temperature phases by structure combination branching processes in the same fashion as in the phase diagram of the ANNNI model.     

Position space renormalization group study of the spin-1 random semi-infinite Blume–Capel model

We study the spin-1 Blume–Capel model under a random crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal–Kadanoff technique. Interesting results are obtained, which tell us that the randomness destroys the first order phase transitions and only those of the second order occur. We give the list of nine fixed points and their topology describing the surface critical behavior. Five new types of phase diagram are found with a rich variety of phase transitions, in accordance with the values of the bulk and surface probabilities and the ratios linking bulk and surface interactions.     

The phase diagram of oxygen ordering in YBa2Cu3O6+δ: The nine point cluster approximation

The thermodynamics of oxygen ordering in the basal plane of YBa₂Cu₃O_6+δ is studied within the nine point approximation of the cluster variation method. The phenomena is modeled by an Ising model with nearest-and next-nearest-neighbor interactions. The composition (δ) versus the temperature (T) phase diagram is calculated and compared with results obtained by using smaller clusters and the Monte Carlo method. The composition dependence of the order parameters for various temperatures is also presented.     

Variat ional-Cumulant Expansion on the Five-State Clock Model

The phase transition of the 5-state dock model has been studied by standard variationalcumulant expansion (VCE) method. We calculated the fiee energy (F) and the internal energy (E) to the fourth order approximation and the specific heat (C) to the third order approximation with the trial action of one variational parameter. The position of the phase transition point given above is in agreement with the results of the Monte Carlo (MC). We also calculated the model to the third order approximation with the trial action of two variational parameters. The comparison of the results for one variational parameter with that for two is given. From this, we can see how the choice of the trial action affects the result and the trial action must be equivalent to the action of the system. All above has shown that the VCE is convergent in the calculation of the 5-state clock model.     

Phase diagram of a nearest neighbor triangular antiferromagnet in an external field

The order-disorder transition in a nearest neighbor antiferromagnetic triangular lattice in a magnetic field is examined using a Monte Carlo method. Comparisons are made with the Kikuchi approximation of Burely. The phase diagram takes the form conjectured by Domb.     

The AB−AC quasi-binary section of the order-disorder phase diagram

The AB?AC sections of the order-disorder phase diagram of a ternary alloy ordered with the L1_o binary superstructure are calculated according to the Kikuchi method in an approximation which enables four-body correlations in the atomic arrangement on the tetrahedron sites to be taken into account. The formation conditions of some ternary superstructures are considered. The change of the character of the order-disorder diagram versus the value and sign of the energy parameters, which reflect the ability of different component atomic pairs to order in the first coordination sphere, is discussed.     

Phase field simulation of microstructure evolution in Fe-Cr-Co alloy during thermal magnetic treatment and step aging

The evolution of modulated structures in Fe-Cr-Co alloys during isothermal aging under an external magnetic field and multiple step aging was simulated based on a phase field method. In this simulation, the magnetic configuration during the decomposition was calculated by a micromagnetic method, and the chemical Gibbs energy function was calculated by the CALPHAD approach based on the experimental equilibrium phase diagram. The calculation results provide a quantitative microstructure change directly linked to the phase diagram and demonstrate obvious microstructure difference between isothermal aging and multiple aging. The ferromagnetic precipitates elongate along the direction of the external magnetic field. The simulated evolution and microstructure are in good agreement with the experimental results.     

Comment on the electron-hole droplet condensation in direct gap semiconductors

The electron-hole droplet nucleation in highly excited direct gap semiconductors is a non-equilibrium phase transition of second order. Within the framework of a Fokker - Planck approximation modifications of the thermodynamic phase diagram and the cluster distribution function are calculated. Due to the short lifetime of the electronic excitations only very small electron - hole clusters can be formed.     

On the magnetic phase diagram of (Mn,Fe)WO4 wolframite

The magnetic phase diagram of mixed crystals of type (Mn, Fe)WO₄ is discusses within molecular field approximation. The two species of magnetic ions tend to align in different orderings. Depending on the interaction strengths the two ordered phases are separated either by a phase in which both orderings are superimposed or by a first order transition.