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     

Phase diagrams for the triangular Ising lattice with re-entrant ferromagnetism

We present the phase diagrams in a 2D spin 1/2 Ising model for the triangular lattice. Using the finitecluster approximation and renormalization technique we studied a nearest-neighbour random interactions. Ferromagnetic exchange interactionsJ are considered with concentrationp and exchange interactions J (||1) with concentration (1-p). The phase diagrams were obtained for this model. They show re-entrant behaviour in certain ranges of the concentrationp and different .     

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 diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart

We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model with fixed couplings in which a “gas of noninteracting dimers (or spin liquid) — ferro or antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. The analysis of the random model is done by applying a recently proposed method which allows us to derive the critical surface of a random model through a mapping with a corresponding nonrandom model.     

Phase diagrams and magnetic properties of diluted Ising and Heisenberg magnets with competing interactions

Ising and Heisenberg magnets with nearest-neighbor ferromagnetic exchangeJ ₁ and next-nearest antiferromagnetic exchangeJ ₂ and randomly distributed frozen-in nonmagnetic impurities of arbitrary concentration 1–x are studied by several methods: systematic series expansions inx, 1–x and inverse temperature (1/T) as well as Monte Carlo simulation. Depending onRJ ₂/J ₁,T andx the model is in paramagnetic, ferromagnetic, antiferromagnetic or spin glass phases. The microscopic magnetic structures of all these phases are investigated and found to be more complicated than usually (e.g., the ferromagnetic state contains spins and clusters either aligned antiparallel or not aligned at all, when frustration effects make bonds ineffective). We suggest that the concentrationx _c of magnetic ions below which no (anti-)ferromagnetic long range order occurs depends onR continuously, andx _c 1 at the multicritical point (R _m ,T=0) where the order changes from ferromagnetic to antiferromagnetic. Our results for phase diagram, susceptibility etc. are compared to recent data on the Eu _x Sr_1–x S system and very good agreement is found.     

Bethe-Peierls approximation for the disordered Ising model

We study the Ising model for an alloy with an arbitrary number of components. We develop an approximation which reduces to that of Bethe and Peierls when the concentration of one of the components is unity. We investigate within this approximation the dependence of the various thermodynamic quantities, in particularT _c, on the composition of the alloy and the magnetic properties of its constituents. Comparison with the only exact calculation available, that of F. T. Leeet al., for a linear chain, shows extremely satisfactory agreement.Research supported by ARO (D). It has also benefited from the general support of Materials Science at the University of Chicago by the NSF.     

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.     

Phase diagram of the antiferromagnetic triangular Ising model with anisotropic interactions

It is argued that there exist two antiferromagnetic phases in the triangular Ising model with anisotropic interactions. A method due to Müller-Hartmann and Zittartz (MZ) is used to derive a closed-form expression for the phase boundary. We also give a criterion under which the MZ method is expected to be applicable and accurate.Work supported in part by a grant from the National Science Foundation.     

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 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.     

横向随机晶场Ising模型的相图和磁化行为研究

在有效场理论和切断近似框架内，选择自旋S=1的二维方格子，研究横向随机晶场Ising模型的相图和磁化行为，重点是横向随机晶场浓度和晶场比率对相图和磁化的影响.给出了i>T-D_x空间的相图和m-T空间的磁化图.在晶场稀疏情况下，负晶场方向存在临界温度的峰值，正方向可出现重入现象.晶场比率取+0.5和-0.5时，磁有序相范围缩小，特别是晶场比率取-0.5时，随晶场浓度的降低，临界温度峰值从横向晶场负方向渡越到正方向.固定某一负晶场值，不同晶场比率的磁化行为有明显差异.同时与纵向稀疏晶场Ising模型结果进行有意义的比较. 关键词： 横向随机晶场Ising模型 相图 磁化行为     

Phase diagrams of a spin-1 Ising superlattice

The three-dimensional spin-1 Ising superlattice consisting of two different ferromagnetic materials with two different crystal fields _Δ1${\Delta }_1$ and _Δ2${\Delta }_2$ is considered in the mean field approximation. The phase diagrams are considered in the (t,_d2$t,d_2$) plane for different ranges of variation of _d1(t=T/J,_d1=_Δ1/J$d_1(t=T/J,d_1={\Delta }_1/J$, _d2=_Δ2/J$d_2={\Delta }_2/J$ are the reduced temperature and crystal fields respectively). The phase diagrams exhibit a variety of multicritical points and reentrant and double reentrant behaviours. They are found to depend qualitatively and/or quantitatively on the thicknesses of the materials in a supercell. This has direct consequences on the nature of the magnetic states of superlattices with different thicknesses.     

Three-dimensional Ising model with four-particle interactions

On the basis of the operational Pfaffian method it is shown that a three-dimensional Ising model with four-particle interactions is reduced to the problem of three interdependent planar lattices and its partition function is expressed through Pfaffian minors of a cyclic matrix.     

Phase diagrams of a mixed-spin hexagonal Ising nanotube with core-shell structure

The Phase diagrams of a ferrimagnetic mixed-spin (1/2, 3/2) hexagonal Ising nanotube with Core-Shell structure are investigated using the mean field approximation. For this, we have studied the effects of the exchange interactions and crystal field on the magnetic properties of the system. The results obtained show the appearance of critical and compensation behaviors, as well as first-order phase transitions terminating at isolated end-points in the ferrimagnetic phase domain at low temperatures.     

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.