Dimensional Heisenberg Model Research Articles

Molecular time scale generalized Langevin equation theory for coupled spin systems

The MTGLE theory is formulated for spin systems using the exact low temperature limit solution of the one dimensional ferromagnetic Heisenberg model as a guide. The final equations are solved to reproduce the exact time correlation function and GLE response function for the spin 1/2 XY model in the high temperature limit [Sur et al., Phys. Rev. B 12, 3845 (1975)]. The advantage of the method is that it can be applied to complex systems with relative ease and in the case of spin systems provides an avenue for investigating effects of anisotropic dipolar spin interactions. One such application to exchange narrowing of the ESR line shape is discussed.

Green's Function Theory of the Two-DimensionalHeisenberg Model–Spin Wave in Short Range Order–

The two dimensional Heisenberg model is studied with a Green's function decoupling scheme in the ferromagnetic and the antiferromagnetic cases. We employ Kondo and Yamaji's formulation and improve it quantitatively. The present theory does not violate the rotational symmetry and the sum rule of the correlation function. We calculate excitation spectrum, long range order, correlation functions, correlation length, energy, and spin susceptibility. The results are compared with those of the Monte Carlo simulations and the experiments of La 2 CuO 4 . Qualitative and semi-quantitative agreements are obtained. In particular, the temperature dependence of the susceptibility indicated by Monte Carlo simulations is reproduced over all temperature region.

Operator renormalization group and spin systems.

The results of a new hybrid method for calculating ground-state energies for lattice Hamiltonians are presented. This method combines the $t$ expansion with the real-space renormalization-group approach, with the hope of extracting infinite-volume physics at $t\ensuremath{\rightarrow}\ensuremath{\infty}$ from calculations of only a few powers of $t$. We calculate the ground-state energy for the (1+1)-dimensional anisotropic Heisenberg model and the (1+1)-dimensional Ising model. Using a blocking that treats the sites and links symmetrically, we were able to determine the exact critical point of the Ising system. In both of these systems we see that the operator renormalization-group method substantially improves upon the results of either the $t$ expansion or real-space renormalization-group methods used separately.

Possible permutation symmetry in two dimensional Heisenberg Model

A method for obtaining the ground state of the two dimensional Heisenberg Model is proposed in terms of permutation operations. First a minimal basis set of spin functions for the ground state is prepared for a given Hamiltonian using the high symmetry of the spin functions. The symmetry of the spin functions can be expressed graphically by permutations commutable with the Hamiltonian. We then solve the Hamiltonian using the minimal basis set whose dimension is much smaller than that of the subspace of singlet states. An analytical solution for the finite system of N = 10 is given.

Monte Carlo simulation of a one dimensional classical Heisenberg model with long range interactions

Abstract We have studied a classical system, consisting of three dimensional unit vectors associated with a one dimensional lattice {u k|k ∈ Z} and interacting via the translationally invariant pair potential This potential model has been proven rigorously to possess a ferromagnetically ordered phase at low but finite temperature. We also consider the pair interaction defined by the two potential models have the same partition function, and essentially the same structural properties, thus V' possesses a low-temperature transition to an anti-ferromagnetically ordered phase. In turn, V' can be regarded as an extreme case of a nematogenic lattice model, whose structural properties can still be evaluated under V. The system was characterized quantitatively by Monte Carlo simulation, whose results are compatible with a second order transition at T*c(=kTc/ε) of 1·48 ± 0·02. Comparison with molecular field and spherical model treatments is also reported; the former, but not the latter, agrees reasonably with the simulation results.

Etude structurale et magnetique d'une phase non stoechiometrique lamellaire du systeme Ga 2S 3-Cr 2S 3, de composition [formula omitted

Structural and magnetic studies of the Ga 2S 3-rich zone of the phase diagram of the Ga 2S 3-Cr 2S 3 system. The layered compound Ga 1.66 CrS 4 is isomorphous with FeGa 2S 4. It has a lamellar structure characterized by an alternative localization, in a host sulfur framework, of Cr, Ga and vacancies in planes perpendicular to the c axis. Each Cr 3+ ion is surrounded by six nearest S neighbours. Magnetic susceptibility versus T curve can be interpreted on the basis of a two dimensional Heisenberg model.

The Effects of Spontaneous Strains at the Dhd-Drd Phase Transition in HAT Series

Abstract Spontaneous strain effects at the Dhd-Drd phase transition in HAT columnar liquid crystal systems are taken into account. The transition is then treated as a paraelasticferroelastic transition, which is known in some crystal systems, but has never been discussed in liquid crystal systems. The anomaly of the elastic compliance near the transition is discussed. The critical exponents remain the same as our previous work, namely those of the three dimensional Heisenberg model with cubic anisotropy.

Phase transitions in anisotropic lattice spin systems

A general method for proving the existence of phase transitions is presented and applied to six nearest neighbor models, both classical and quantum mechanical, on the two dimensional square lattice. Included are some two dimensional Heisenberg models. All models are anisotropic in the sense that the groundstate is only finitely degenerate. Using our method which combines a Peierls argument with reflection positivity, i.e. chessboard estimates, and the principle of exponential localization we show that five of them have long range order at sufficiently low temperature. A possible exception is the quantum mechanical, anisotropic Heisenberg ferromagnet for which reflection positivity isnot proved, but for which the rest of the proof is valid.

Etude par effet Mössbauer de Ca 2MnO 4 dope a l'etain

The antiferromagnetic layer phase Ca 2MnO 4 doped with 119Sn 4+ has been investigated by Mössbauer spectroscopy. Below the Néel temperature a hyperfine magnetic field transfered on the tin nucleus is observed with saturation value H(0)≅38 kOe. The low value of the transfered field is attributed to the absence of e g electrons on the 3 d orbitals of Mn 4+. Supposing the field to follow the power law H( T) = H(0) D[1 − ( T/ T N )] β as the sublattice magnetizations usually do, the study of the temperature dependence of the field yields β = 0.44 ± 0.10. This value for the critical exponent is in rather good agreement with the value deduced from neutron measurements ( β = 0.38 ± 0.06) as well as with those calculated from three dimensional Heisenberg and Ising models (0.31⩽β⩽0.38). It is anyway very different from the theoretical value for a two dimensional Ising model ( β = 0.125) and from the experimental values for various two-dimensional antiferromagnets isostructural with Ca 2MnO 4 such as K 2MnF 4 ( β = 0.15) or K 2NiF 4 ( β = 0.14).

Crystal structure of the compounds A 2MnX 4−xX′ x (A = NH 4, Rb, Cs; X = Cl; X′ = Br, I; x = 0, 1, 2) and magnetic susceptibility of A 2MnCl 4 (A = Rb, Cs)

Of the compounds A 2 MnCl 4 (A = Rb, Cs), it is known that they crystallize in the K 2 NiF 4 structure. We have investigated a number of compounds A 2 MnX 4-x X′ x with A = NH 4 , Rb, C 3 , X = Cl, X′ = Br, I and x = 0, 1, 2. By means of X-ray powder diffraction it is determined, that these compounds also have the K 2 NiF 4 structure. The X′ ions occupy special sites in the crystal lattice. The unit cell parameters of all compounds prepared are given. Susceptibility data are obtained for Rb 2 MnCl 4 and CsMnCl 4 . The susceptibility is interpreted on the basis of the two dimensional antiferromagnetic Heisenberg model. The intralayer exchange constant is J/k = −6.2 K and −5.0 K for Rb 2 MnCl 4 and Cs 2 MnCl 4 , respectively.

Application of a procedure of Shanks to the calculation of critical exponents

We apply a procedure due to Shanks to the ϵ-expansion of Brezin et al. for the critical exponent γ of the three- dimensional Ising and Heisenberg models.

Effective long range order and phase transitions in finite, macroscopic one and two dimensional systems

The concept of long range order is discussed for finite macroscopic systems. It is shown that if the interaction range or strength, in units of kT, is of O(log N), long range order is obtained in one dimensional systems. Short range and long range interactions are able to combine to cause long range order even when each of the two interactions by itself is much too weak to do so. A physical picture of the effects of the long range interactions is presented and supported by detailed calculations. We also show that the theorem stating that the two dimensional Heisenberg Model does not exhibit long range order is inapplicable when the interaction strength in units kT is of O(log N), or when the range of the interaction is of O( log N) 1 4 . The two dimensional Bose gas will condense at temperatures of O( T 0 log N ) , where T 0 is the condensation temperature in three dimensions. The recent proof that superfluid long range order is impossible in two dimensions, is shown to be based, for finite N, on the analogous fact in the free gas, which is invalid according to the above. Consideration of thin Bose films shows that the transition from three dimensional (condensation at T 0) to two dimensional (condensation below T 0) behavior occurs at film thickness of order log N. This result can be of practical importance.

A Note on the Ground State of Antiferromagnetism

Kasteleijn's method of obtaining the ground state of antiferromagnetism is generalized to the cases of two and three dimensional lattices. According to our generalization, the ground state of the three dimensional antiferromagnetic Heisenberg model with the spin quantum number equal to one half is paramagnetic in the absence of anisotropy energy. The magnetization of sublattices is calculated as a function of the degree of anisotropy. With increasing coordination numbers the anisotropy energy necessary for establishing the antiferromagnetic state decreases rapidly.