Magnetic specific heat of the honeycomb lattice of spin one-half with anisotropic Heisenberg exchange by a new method

The magnetic specific heat of the honeycomb lattice of $\text{S =}\text{1}\text{2}$ Heisenberg spin with anisotropic exchange is calculated by using the new approximation method reported in a previous paper. In the spin system with the anisotropy parameter |γ|<1 (Ising-Heisenberg system), the specific heat shows a similar divergence as that of the pure Ising spin system, namely a logarithmic divergence at the critical temperature. The same approximation is also applied to the spin system with |γ|>1 (Heisenberg XY system), showing a divergence of the same kind.     

Thermodynamics of the two-dimensional ferromagnetic Heisenberg spin systems

The problem of the title is studied by means of the Green function formalism with decoupling at a stage one-step further than Tyablikov's theory. At low temperatures the specific heat is proportional to the temperature T and the magnetic susceptibility to exp (constant/T)/T.     

The magnetic properties of the two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field

The two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field is studied by means of the double-time Green's function. The analytic expressions of the critical temperature, the high-temperature zero-field susceptibilities, the spin-wave velocity, spin-wave stiffness and spin-wave gap are obtained. The phase diagrams in which the critical temperature, the reorientation temperature and the reorientation magnetic field are shown as a function of single-ion anisotropic parameter are discussed.     

Absence of spontaneous magnetic order at nonzero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactions

The Mermin-Wagner theorem is strengthened so as to rule out magnetic long-range order at T > 0 in one- or two-dimensional Heisenberg and XY systems with long-range interactions decreasing as R(-alpha) with a sufficiently large exponent alpha. For oscillatory interactions, ferromagnetic long-range order at T > 0 is ruled out if alpha > or = 1(D = 1) or alpha > 5/2(D = 2). For systems with monotonically decreasing interactions, ferro- or antiferromagnetic long-range order at T > 0 is ruled out if alpha > or = 2D.     

Spin-ordering in S = 1 anisotropic Heisenberg models with nondiagonal spin exchange

The properties of S = 1 anisotropic Heisenberg models with nondiagonal exchange between axial and planar spin components are investigated using Monte Carlo techniques. The quantum nature is taken into account in a semi-classical approximation. The ordering of the spins when applying an external field with axial and planar components is discussed. It is argued that the quantum nature of the spins and the nondiagonal exchange may explain the peculiar shape of the magnetic specific heat of FeBr₂ as well as the weakly first-order phase transition observed in the same compound when a tilted field is applied. Received 24 January 1999     

Coherent Exchange Cluster Approach for two-dimensional disordered Heisenberg spin systems

The spin wave properties of disordered two-dimensional and quasi two-dimensional Heisenberg spin systems, with an antiferromagnetic ground state (Neèl state) induced by single-ion anisotropy, are discussed within a Coherent Exchange Cluster Approach (Cluster CEA).The configuration averaged Green's functions are described by an effective spin wave Hamiltonian, with two sets of complex and energy dependent coherent exchange integralsJ _lm ¹ (E) andJ _lm ² (E) appropriate to the consideration of two different spins of the binary alloy constituents.J _lm ¹ andJ _lm ² , depending only on the distance of the sitesl andm, are taken to be non zero only for nearest neighbours. The remaining two quantitiesJ ¹(E) andJ ²(E) are determined self-consistently from the requirement that the most important matrix elements of the scatteringT matrix vanish when the configuration averaging has been performed.Numerical results are presented for the antiferromagnetic quasi two-dimensional systems K₂Ni _c Mn_1-c F₄ and Rb₂Fe _c Mn_1-c F₄.Both the density of states and the transverse susceptibilities, determining essentially the neutron scattering cross-sections, are calculated.The density of spin wave states for K₂Ni _c Mn_1-c F₄ is compared for different concentrations with exact computer calculations for finite 30 × 30 arrays. The agreement is excellent.Based on the thesis of H.J. Schlichting, Fachbereich Physik der Universität Hamburg, 1974.     

Coherent Exchange Cluster Approach for two-dimensional disordered Heisenberg spin systems

The spin wave properties of disordered two-dimensional and quasi two-dimensional disordered Heisenberg spin systems, with a ferromagnetic ground state induced by single-ion anisotropy, are discussed within a Coherent Exchange Cluster Approach (Cluster CEA). The configuration averaged Green's function is described by an effective spin wave Hamiltonian, with complex and energy dependent coherent exchange integrals , where, depends only on the distance of the sitesl andm Considering only nearest neighbour clusters, the more distant exchange is neglected, whereas the nearest neighbour coherent exchange integral is determined by the self-consistency requirement that the most important matrix elements of the scatteringT matrix vanish when the configuration averaging has been performed. The approximations inherent within this approach are discussed, and it is argued that it is practically impossible to improve it essentially.The results of numerical calculations for the square lattice are presented: The parameters have been chosen as to discuss, in a somewhat hypothetical way, the properties of Fe–Ni monolayers on a Cu substrate, especially for dominating Fe concentration, where experiments are still lacking. In contrast to the oversimplified standard Single Bond CEA, the Cluster CEA yields a considerable structure within the density of states. Furthermore, for the almost dilute case, with Ni concentrationc _Ni=0.2 and exchange integralsJ _{Ni, Fe}=2.5·J _{Ni, Ni},J _{Fe, Fe}=0.3·J _{Ni, Ni}, there is even a gap, as expected from exact calculations for isolated impurities. Even within this case, the Green's functions and self-energies are analytic, in contrast to certain generalizations of the well-known CPA method for electronic systems.Concerning the critical concentrations for the appearance of a spin wave instability with negative Fe–Fe exchange, the Cluster CEA yields much better results than the Single Bond CEA.     

Thermodynamic properties of Heisenberg magnetic systems

In this paper, we present a comprehensive investigation of the effects of the transverse correlation function （TCF） on the thermodynamic properties of Heisenberg antiferromagnetic （AFM） and ferromagnetic （FM） systems with cubic lattices. The TCF of an FM system is positive and increases with temperature, while that of an AFM system is negative and decreases with temperature. The TCF lowers internal energy, entropy and specific heat. It always raises the free energy of an FM system but raises that of an AFM system only above a specific temperature when the spin quantum number is S 〉 1. Comparisons between the effects of the TCFs on the FM and AFM systems are made where possible.     

Solitons and spin complexes in the anisotropic Heisenberg chain

It is shown that in the case of the spin chain with weak anisotropy the quasiclassical energies of the soliton solutions of the Landau-Lifshitz equation coincide with the magnon bound state energies.     

Replica symmetry breaking transition of the weakly anisotropic Heisenberg spin glass in magnetic fields

The spin and the chirality orderings of the three-dimensional Heisenberg spin glass with the weak random anisotropy are studied under applied magnetic fields by equilibrium Monte Carlo simulations. A replica symmetry breaking transition occurs in the chiral sector accompanied by the simultaneous spin-glass order. The ordering behavior differs significantly from that of the Ising spin glass, despite the similarity in the global symmetry. Our observation is consistent with the spin-chirality decoupling-recoupling scenario of a spin-glass transition.     

Modeling a dimer state in CuGeO3 in the two-dimensional anisotropic Heisenberg model with alternated exchange interaction

The two-dimensional Heisenberg spin-1/2 model with alternated exchange interaction along the c axis and an anisotropic distribution of the exchange interaction in the lattice, J _b/J _c=0.1, is examined. A quantum Monte Carlo method is used to calculate the phase diagrams of the antiferromagnet, the dimer state in a plane, the value of the alternation δ of the exchange interaction, and the anisotropy Δ=1−J ^xy/J ^z of the exchange interaction, Δ∼δ ^0.58(6). The following characteristics are calculated for Δ=0.25: the dependence of the temperature of the dimer-state-paramagnet transition on the alternation of the exchange interaction, T _c(δ)=0.55(4)(δ−0.082(6))^0.50(3), the singlet-triplet energy gap, and the dependence of the magnetization on the external field for some values of δ. The value of the exchange interaction, J _c=127 K, the alternation of the exchange interaction, δ=0.11J _c, and the correlation radius along the c axis, ξ _c≈28c, are determined. Finally, it is found that the temperature dependence of the susceptibility and the specific heat are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 112, 2184–2197 (December 1997)     

Renormalization group approach to the phase diagram of two-dimensional Heisenberg spin systems

A renormalization group method is used to analyse the phase diagram of a quantum-mechanical Hamiltonian version of the O(2) and O(3) Heisenberg spin systems in two dimensions. It shows a phase transition at non-zero coupling for the O(2) model and no evidence of it for the O(3) model.     

Vortices and magnetic structures of the target type in a two-dimensional ferromagnet with anisotropic exchange

Various types of magnetic structure in a two-dimensional Heisenberg ferromagnet are considered in a continuum approximation. The effect of anisotropic exchange and single-ion anisotropy on the vortex structure is analyzed. A new type of static magnetic structure (“target”) is predicted and investigated in an easy-plane ferromagnet.     

The mermin-wagner phenomenon and cluster properties of one- and two-dimensional systems

We give optimal conditions concerning the range of interactions for the absence of spontaneous breakdown of continuous symmetries for one- and two-dimensional quantum and classical lattice and continuum systems. For a class of models verifying infrared bounds our conditions are necessary and sufficient. Using the same techniques we obtain a priori bounds on clustering for systems with continuous symmetry, improving results of Jasnow and Fisher.Partially supported by CAPES-PICD.Partially supported by the CNP_q.Partially supported by N.S.F. under grant MCS 7801433.     

Spin transport in the anisotropic easy-plane two-dimensional Heisenberg antiferromagnet

Spin transport in the easy-plane two-dimensional anisotropic Heisenberg antiferromagnet with S=1 is studied. Regular part of spin conductivity is calculated, at zero temperature, using a self-consistent harmonic approximation and the Kubo formalism. Three magnon processes provide the dominant contribution to the spin conductivity. Furthermore, the transport is ballistic and characterized by finite Drude weight.     

Dimer state in the two-dimensional anisotropic alternated-exchange Heisenberg model

An analysis is made of the two-dimensional Heisenberg model with S=1/2, anisotropic exchange interaction between nearest neighbors, and alternating exchange in two directions, [100] and [010] (corresponding to condensation of the (π, π) mode) and in one direction [100] (corresponding to condensation of the (π, 0) mode). The quantum Monte Carlo method is used to calculate the thermodynamic characteristics and the spin correlation functions which are used as the basis to determine the boundary of stability of an anisotropic antiferromagnetic with respect to alternation of exchange δ=(1−J ^x,y /J ^z )^0.4 in the (π,π) model and δ=(1−J ^x,y /J ^z )^0.31 in the (π,0) model. In the (π,0) model a disordered quantum state exists in the range (1−J ^x,y /J ^z )^0.31<δ<(0.3–0.35). The energy (E−0.68)=0.36δ ^1.80(6) and 0.21 δ ^2.0(5), the energy gap between the ground and excited states H _c (δ)=1.96δ ^2.(1), 1.8(1) (δ−0.35(3))^0.67(2) were determined as a function of the alternation of exchange in the (π,π)-and (π,0) models, respectively. Fiz. Tverd. Tela (St. Petersburg) 40, 1080–1085 (June 1998)     

The quantum correlation of anisotropic Heisenberg spin chain under the control of inhomogeneous magnetic field

The quantum correlation (quantum entanglement and quantum discord)’s dynamical behavior characteristics of Heisenberg XXZ spin chain with Dzyaloshinskii–Moriya (DM) interaction heterogeneous magnetic field that manipulated by sinusoidal wave are investigated in this paper. The results indicate that quantum correlation of anisotropic Heisenberg XXZ spin chain can be regulated effectively by magnetic field intensity B and magnetic field uniformity cos θ   of the external magnetic field. Under the effects of DM interaction in qubits, the quantum correlation's dynamics evolution process appears sudden death and birth. But DM interaction has a critical value D_CZ$D_{CZ}$ which is connected with other quantum correlation versus parameters. Only when Dz≥D_CZ$D_z\ge D_{CZ}$, sudden death and birth can be obviously observed under the rest given parameters.     

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (_Tc)$(T_{\mathrm{c}})$ in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L$L\times L$ square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K$K$ limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of _Tc$T_{\mathrm{c}}$ on anisotropic parameter K$K$ becomes linear and in the single-ion anisotropic case, _Tc$T_{\mathrm{c}}$ becomes independent of K$K$. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125$\alpha =0.125$ and γ=1.75$\gamma =1.75$.