Decorated Ising Model Research Articles

Phase diagram and ground state of the decorated Ising model on a triangular lattice with first neighbor antiferromagnetic and second neighbor ferromagnetic interactions

Phase diagram and ground state of the decorated Ising model on a triangular lattice with first neighbor antiferromagnetic and second neighbor ferromagnetic interactions

Reentrant phenomenon in the decorated ising model

Based on the transverse-field Ising model, this paper utilizes the theory of correlated effective fields to explore the ferromagnetic phase transition properties of nanoislands with decorated lattice. The findings suggest that the unique phase transition properties of the system are predominantly determined by the surface atoms, while the transverse field and decorating exchange interaction impact the specific details of the phase transition properties. Additionally, the magnetization of each lattice follows a quantitative relationship, in which the magnetization of the decorated lattice is weaker and that of the central lattice is stronger.

Phase Diagram and the Ground State of the Decorated Ising Model on a Triangular Lattice with Ferromagnetic Interaction between the First Nearest Neighbors and Antiferromagnetic Interaction between the Next Nearest Neighbors

Phase Diagram and the Ground State of the Decorated Ising Model on a Triangular Lattice with Ferromagnetic Interaction between the First Nearest Neighbors and Antiferromagnetic Interaction between the Next Nearest Neighbors

Phase Diagram and Ground State of a Decorated Ising Model on a Cubic Lattice

Phase Diagram and Ground State of a Decorated Ising Model on a Cubic Lattice

Critical properties of an antiferromagnetic decorated Ising model on a square lattice

The authors have investigated the static critical behavior of a two-dimensional decorated Ising model on a square lattice in an external magnetic field, using computational physics methods. Particular consideration has been given to a special case when antiferromagnetic exchange interaction is observed only between decorated spins and spins located at lattice sites. It has been shown that at an external magnetic field of H0 = 4, the model experiences partial degeneracy in the ground state. At field values close to H0 = 4, heat-capacity splitting is observed.

Thermodynamics properties of copper-oxide superconductors described by an Ising frustrated model

In this work we will study the thermodynamics properties of the quenched decorated Ising model with competitive interactions through the effective field theory (EFT) of a one-spin cluster. This model is used here to describe the thermodynamics properties of the cooper-based oxide superconductors compounds in its insulating phase (antiferromagnetic). The model consists of planes in which the nodal spins interact antiferromagnetically (JA<0) with their nearest-neighbors and ferromagnetically (JF>0) with the spins that decorated the bonds, which are quenched randomly distributed over the two-dimensional lattice. The planes interact antiferromagnetically with weak exchange interaction (i.e., JA′=λJA, λ=10−5). By using the framework of an effective-field theory, based on the differential operator technique, we discuss beyond thermodynamics properties the antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space (T×p), for λ=10−5 and various values of frustration parameter (α=JA/JF), magnetic field (H) and concentration parameter (p). For certain range of the parameter α we observe a reentrant behavior in low-temperature that it reflects in the properties behavior itself.

Dysprosium-based experimental representatives of an Ising-Heisenberg chain and a decorated Ising ring

It is shown that the bond-decorated Ising model is a realistic model for certain real magnetic compounds containing lanthanide ions. The lanthanide ion plays the role of Ising spin. The required conditions on the crystal-field spectrum of the lanthanide ion for the model to be valid are discussed and found to be in agreement with several recent ab initio calculations on Dy(III) centers. Similarities and differences between the spectra of the simple Ising chain and the decorated Ising chain are discussed and illustrated, with attention to level crossings in a magnetic field. The magnetic properties of two actual examples (a [DyCuMoCu] chain and a Dy4Cr4 ring) are obtained by a transfer-matrix solution of the decorated Ising model. g-factors of the metal ions are directly imported from ab initio results, while exchange coupling constants are fitted to experiment. Agreement with experiment is found to be satisfactory, provided one includes a correction (from ab initio results) for susceptibility and magnetization to account for the presence of excited Kramers doublets on Dy(III).

Generalized transformation for decorated spin models

Abstract The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [ − s , s ] is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising model. We apply this transformation to a particular mixed spin-(1/2, 1) and (1/2, 2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin- S square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also includes combinations of three-body and four-body interactions; in particular we considered spin 1 and 2.

Thermodynamic properties of the exactly solvable mixed spin-S and spin- [formula omitted] Ising model with four-spin interactions on doubly decorated planar lattices

The exact solution of the doubly decorated Ising model with two- and four-spin interactions and crystal-field anisotropy is obtained using the generalized mapping transformation technique. Within this scheme, the exact relations for the phase boundaries, compensation points and spontaneous magnetization are derived for different planar lattices with the arbitrary values of the decorating spins. The particular attention has been paid to the investigation of the reentrant behaviour in the system. The region in which the reentrant behaviour and compensation phenomena occur in the system is studied in detail.

Frustrated model to describe reentrant behavior in copper oxide superconductors

The quenched decorated Ising model with competitive interactions is used here to described the magnetic properties of the copper oxide superconductors compounds in the insulating phase (antiferromagnetic). The model consists of planes in which the nodal spins interact antiferromagnetically ( J A < 0 ) with their nearest-neighbors, and ferromagnetically ( J F > 0 ) with the spins that decorate the bonds, which are quenched and distributed randomly over the two-dimensional lattice. The planes interact antiferromagnetically with weak-exchange interaction (i.e., J A ′ = λ J A , λ = 10 - 5 ). By using the framework of an effective-field theory, based on the differential operator technique, we discuss the antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space ( T - p ), for λ = 10 - 5 and various values of frustration parameter α = J A / J F . For certain region range of the parameter α we observe a reentrant behavior at low-temperature. We also discuss the critical behavior of T N versus α for some values of decorated bond concentrations and reentrant phenomena is observed. We calculate the dependence of the staggered magnetization as a function of the temperature to analyze the reentrant behavior observed in the phase diagrams.

Ferrimagnetism and compensation points in a decorated 3D Ising models

We give a precise numerical solution for decorated Ising models on the simple cubic lattice which show ferromagnetism, compensation points, and reentrant behaviour. The models, consisting of S= 1 2 spins on a simple cubic lattice, and decorating S=1 or S= 3 2 spins on the bonds, can be mapped exactly onto the normal spin- 1 2 Ising model, whose properties are well known.

Exact results of a doubly decorated ising model with four-spin interactions

A doubly decorated Ising model with the crystal-field, two—and four-spin interactions is studied by applying the standard decoration-iteration transformation. Exact results for the critical boundaries, compensation temperatures and magnetization of the system are discussed in detail.

Some characteristic properties of a decorated ferrimagnetic Ising system

The magnetic properties (phase diagram, magnetization curve, spin correlation functions, internal energy and magnetic specific heat) of a decorated ferrimagnetic square lattice composed of three magnetic atoms are investigated on the basis of the differential technique. The system can show many interesting properties which have not been obtained in the previous decorated Ising models. In particular, the possibility of two compensation points can be found more easily than that of the previous systems discussed in J. Phys. Soc. Jpn. 70 (2001) 884 and the specific heat of the present system exhibits various characteristic features in the ordered phase below its transition temperature, depending on the spin of decorated atom and the value of uniaxial anisotropy parameter.

Quenched decorated Ising model in three dimensions

The three-dimensional (3d) quenched decorated Ising model with competitive interactions is treated to simulate the 3d antiferromagnetic phase stability limit of the high-temperature superconductor cuprate compounds (e.g., La–Ba–Cu–O and Y–Ba–Cu–O). The model consists of planes in which the nodal spins interact antiferromagnetically ( J) with its nearest neighbors and ferromagnetically ( K) with a decorated spin on the bond between them, which is quenched and randomly distributed over the lattice. By using the framework of an effective-field theory, we discuss the variation of the critical concentration p c where the Néel temperature tends to zero for various values of α= J/ K. We obtain for α < 1 6 the critical concentration p c=0.0297 in excellent accordance with experimental result p c=0.0250 of the La 2− x Ba x CuO 4 ( x=2 p) compound (2-1-4). Whereas for the YBa 2Cu 3O 6+ x compound (1-2-3) we have obtained a better value p c=0.1588 ( p c exp=0.20) for α= 1 2 . Comparison with the experimental result of the phase diagram also was presented, and it is qualitatively in accordance only for the 1-2-3 compound.

Phase diagram and phase separation of cuprate oxides in decorated Ising model

In application to lanthanum cuprates the Ising model with random antiferromagnetic (AF) and ferromagnetic (FM) interactions between Cu atoms in CuO 2 layers is investigated by the mean-field approximation. The effective interaction between holes as well as their participation in a formation of the intermediate oxygen valency of CuO 2 layer are taken into account. In the phase diagram temperature–hole concentration which exhibits a range of phase separation and contains the critical point AF phase with low hole concentration, AF phase with rich hole concentration is found. Depending on doping level the suggested model describes both the absence of phase separation and the separation into paramagnetic (PM)–AF, PM–FM, and AF–FM phases.

Exact results for a decorated Ising model

Exact results for the phase diagrams, compensation temperatures and magnetizations of a decorated ferrimagnetic Ising model on the square lattice are obtained and discussed.

Antiferromagnetic phase breakdown of a randomly decorated Heisenberg model: Application to La2−xBaxCuO3 (abstract)

The quenched decorated Ising model with competitive interactions recently introduced by Fittipaldi et al.1 is herein extended to the Heisenberg case. The model consists of planes in which the nodal spins interact antiferromagnetically (J&amp;lt;0) with their nearest neighbors, and ferromagnetically (K&amp;gt;0) with the spins that decorate the bonds, which are quenched randomly distributed over the lattice. The planes, which simulate the CuO2 layers in doped cuprates superconducting materials, interact antiferromagnetically (J′=λJ). By using the framework of an effective-field theory with correlations, we discuss the 3D antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space (T−p), for various values of both interplane and intraplane exchange parameters λ and α=|J|/K, respectively. In particular, our numerical estimates of the vanishing temperature critical concentrations pc [i.e., pc at which TN(pc)=0] well compare with the experimental data of Kitaoka et al.2 for the La2−xBaxCuO4 in the nonsuperconducting phase.

Ferrimagnetism in a decorated Ising model

The magnetic properties of a decorated two-sublattice ferrimagnetic Ising model consisting of two magnetic atoms A and B with spins S A (S A = 1 2 ) and S B (S B > 1 2 ) are investigated within the framework of the effective-field theory with correlations. The uniaxial crystal-field interaction D exists on the B atoms and the effects of S B and D on the magnetic properties are examined. We find a number of characteristic phenomena in these quantities, such as the possibility of two compensation points and the two (or three) transition temperatures, not predicted in the Neel theory.

Randomly decorated Ising model on the square lattice

The two-dimensional Ising model decorated with Ising spins of magnitudes s = 1 and 12 is considered. The bonds are randomly decorated with n spins and the random variable is supposed to satisfy an annealed distribution. The model is exactly solved by mapping it onto an effective 2D Ising model. The phase diagram is determined and the lim n → ∞ is discussed.

Phase diagrams of a quenched decorated Ising model with competing interactions

We study a quenched bond-decorated Ising model, on a square lattice, in which the nodal spins interact antiferromagnetically ( J<0) with its nearest neighbors and ferromagnetically ( K>0) with a decorated spin on the bond between them, which is randomly distributed over the lattice. We discuss, within the effective-field approach with correlation, the phase diagrams in both T− p and T−α spaces, where p is the decorated bond concentration and α the competing parameter α=| J|/ K. It is pointed out that the present results may possibly have some relevance to elucidate the experimentally observed magnetic phase diagram of the planar superconducting material La 2− xBa x CuO 4 in the insulating phase.