Phase diagrams of Ising films with competing interactions

The axial next-nearest-neighbour Ising (ANNNI) model of finite thickness is studied. Using mean-field theory, Monte Carlo simulations, and low-temperature analyses, phase diagrams are determined, with a distinct phase diagram for each film thickness. The robustness of the phase diagrams against varying the couplings in the surface layers is analysed. Received 19 March 2002 and Received in final form 2 April 2002 Published online 6 June 2002     

Critical behavior of diluted Heisenberg ferromagnets with competing interactions

The pure and the site-diluted classical Heisenberg model on the face centered cubic (fcc) lattice with ferromagnetic exchange J_nn between nearest neighbors and antiferromagnetic exchange J_nn = −J_nn/2 between next nearest neighbors is studied by Monte Carlo simulation. Data are generated by the heat bath algorithm for lattice sizes L = 4, 8, 12, 16, 20 and 24, using histogram reweighting techniques and sampling up to several hundred configurations of the random site disorder. From a finite size scaling analysis both the critical temperature and the critical exponents are estimated. For the pure system, the data are in very good agreement with the critical exponent estimates 1/v ≈ 1.42, β/v ≈ 0.51 obtained from other methods (as a check of the accuracy of our approach, we also study the nearest neighbor model — where J_nn ≡ 0− and again obtain very good agreement with the known behavior). However, for the diluted systems evidence for a new universality class is found. While for concentration c = 0.875 of occupied sites strong crossover phenomena preclude us from giving exponent estimates, for c = 0.75 we find 1/v ≈ 1.2 and β/v ≈ 0.45. Possible reasons why the Harris criterion may not apply for this system are discussed. The application of this study to experiments on Eu_xSr_1−xS is briefly mentioned.     

Exact results for the diluted Ising model with competing interactions

We consider the random-bond Ising model with the exchange integrals J > 0, ?J and 0 with the respective probabilities p, q and r, where p + q + r = 1. We give the exact value of the averaged internal energy and an exact upper bound to the averaged specific heat at temperature T determined by $\text{k}{}_{\mathrm{B}}\text{T =}\text{2J}\text{In[}\text{p}\text{(1 ? p ? r)}\text{]}\text{,}$ where k_B is the Boltsmann constant. We show that all the averaged correlation functions of even spins are non-negative at this temperature.     

Phase diagram of the Ising square lattice with competing interactions

We restudy the phase diagram of the 2D-Ising model with competing interactions J₁ on nearest neighbour and J₂ on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the criticalpoint at J₂ = J₁/2. Further on we investigate the character of the different phase boundariesand find that the transition is weakly first order formoderate J₂ > J₁/2.     

Phase diagram of the two-dimensional Ising model with random competing interactions

An Ising model with ferromagnetic nearest-neighbor interactions J₁ (J₁>0) and random next-nearest-neighbor interactions [+J₂ with probability p and −J₂ with probability (1−p); J₂>0] is studied within the framework of an effective-field theory based on the differential-operator technique. The order parameters are calculated, considering finite clusters with n=1,2, and 4 spins, using the standard approximation of neglecting correlations. A phase diagram is obtained in the plane temperature versus p, for the particular case J₁=J₂, showing both superantiferromagnetic (low p) and ferromagnetic (higher values of p) orderings at low temperatures.     

Critical properties of the anisotropic Ising model with competing interactions

The critical properties of the anisotropic Ising model with competing interactions have been investigated by Monte Carlo methods. The region of localization of the Lifshitz point on the phase diagram has been computed. Relations of the finite-size scaling theory are used to calculate the critical exponents of the heat capacity, susceptibility, and magnetization at various values of the competing interaction parameter J ₁. A crossover to a critical behavior characteristic of a multicritical point with increasing parameter J ₁ is shown to be present in the system.     

Phase diagrams of spin-1 Ising model with bilinear and quadrupolar interactions under magnetic field. Two-particle cluster approximation

The spin-1 Ising model with bilinear and quadrupolar short-range interactions under magnetic field is investigated within the two-particle cluster approximation. It is shown that for those values of the quadrupolar interaction when at zero magnetic field the system undergoes a temperature phase transition between quadrupolar and paramagnetic phases, a triple point may exist in the temperature vs. magnetic field phase diagrams, necessarily along with a critical point. It is also shown that the critical points in the temperature vs. magnetic field phase diagrams of the investigated model can be of three types.     

Phase diagrams of Ising fluids with Yukawa-Lennard-Jones interactions from an integral equation approach

An integral equation approach is developed to investigate phase coexistence properties of Ising spin fluids with Yukawa ferromagnetic and Lennard-Jones nonmagnetic interactions in the presence of an external field. The calculations are carried out on the basis of the Duh and Henderson closure with a specific Duh-like partitioning of the total potential. The coupled set of the Ornstein-Zernike equation, the closure relation and the external field constraint are solved using an efficient numerical algorithm. The phase diagrams are evaluated in a wide range of varying the external field and the ratio of strengths of Yukawa to Lennard-Jones interactions. Different types of the phase diagram topology as well as various external field dependencies of critical temperatures and densities are identified. The complexity with respect to simple Lennard-Jones fluids is explained by coupling between spatial and spin degrees of freedom in the system. A comparison of the obtained theoretical results with simulation data is made and a good agreement is observed.     

Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

Phase diagram of the Ising Model on a Cayley tree in the presence of competing interactions and magnetic field

We study the phase diagram for the Ising Model on a Cayley tree with competing nearest-neighbor interactionsJ ₁ and next-nearest-neighbor interactionsJ ₂ andJ ₃ in the presence of an external magnetic field. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular cases, previous works by Vannimenus and by Inawashiroet al. At vanishing temperature, the phase diagram is fully determined, for all values and signs ofJ ₂/J ₁ andJ ₃/J ₂; in particular, we verify that values ofJ ₃/J ₂ high enough favor the paramagnetic phase. At finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into two disconnected pieces, etc.) are exhibited for typical values ofJ ₂/J ₁ andJ ₃/J ₂.Partially supported by the Brazilian Agencies CNPq and FINEP.     

Ising model with competing interactions on a Cayley tree

An iterative scheme is developed for a renormalized effective nearest-neighbor couplingK _r and effective field per siteK _r for spins in therth shell of a Cayley tree with nearest neighborJ, and next nearest neighborJ′, interactions between Ising spins on the lattice. In addition to the expected paramagnetic, ferromagnetic, and antiferromagnetic phases, we find an intermediate range ofJ'/J < 0 values whereX _r, and K_r iterate to a continuous or quasicontinuous attractor in theX-K plane. In this range the local magnetization is mainly chaotic with oscillatory glasslike behavior. Embedded in the chaos, however, are regions of periodic and commensurate phases.     

Correlation functions of pure and diluted Ising magnets in the mean-field approximation

A mean-field method, which is a variant of the fixed-scale renormalization group transformation and is applied to both pure and diluted magnets, has been considered. It has been shown that, for pure magnets, the method is equivalent to the Bethe approximation. This method has been used to calculate the magnetization and correlation functions of both pure and bond-diluted Ising magnets.     

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.     

Phase diagrams of a transverse Ising nanowire

Phase diagrams of a cylindrical nanowire described by the transverse Ising model are investigated by the use of two theoretical frameworks, namely the mean field theory and the effective field theory with correlations. The phase diagram of the system is strongly affected by the surface situations. Some characteristic phenomena are found in the phase diagram, depending on the ratio of the physical parameters in the surface shell and the core.     

Spiral magnetic structure in Heisenberg and non-Heisenberg magnets

The possibility of forming a modulated (spiral) magnetic structure in anisotropic Heisenberg and non-Heisenberg magnets with a frustrated Heisenberg exchange interaction has been investigated. It has been demonstrated that, apart from homogeneous (ferromagnetic and quadrupole) states, the Heisenberg magnets with a strong easy-plane anisotropy can have a spiral magnetic structure. The axis of the spiral coincides with the direction of the external magnetic field. The inclusion of the biquadratic exchange interaction leads to a narrowing of the magnetic field region of the existence of the spiral structure. In the absence of the external magnetic field, the spiral structure can be formed only in the case of easy-axis anisotropy.     

Phase distribution and computed magnetic properties of high-remanent composite magnets

Numerical micromagnetic calculations using finite-element techniques allow a quantitative treatment of the correlation between the microstructure and the basic magnetic properties of two-phase permanent magnets such as the remanence, the coercive field and the maximum energy product. For the investigation of (A) the role of the amount of the soft magnetic phase, and (B) the effect of grain shape, realistic three-dimensional grain arrangements have been used. The numerical results show that both short-range exchange and long-range magnetostatic interactions determine the magnetic properties. The optimal microstructure of an isotropic nanocrystalline permanent magnet was found to consist of soft magnetic particles with a large spontaneous magnetization embedded between hard magnetic grains. Exchange interactions than enhance the remanence of isotropic, composite magnets of Nd₂Fe₁₄B and -Fe by about 60%. Because of exchange hardening the soft magnetic phase can be increased up to 50% without a significant loss of coercivity. A uniform grain structure suppresses strong demagnetizing fields and this increases coercivity by 30% as compared with irregular shaped particles.