Study of the ferromagnetic transition in a positionally frozen Heisenberg spin system

Using extensive Monte Carlo simulations with both particle and cluster orientational moves, in conjunction with finite size scaling and histogram reweighting techniques, we have determined the Curie temperature for two models of positionally frozen Heisenberg spin systems: a system with spatial correlations corresponding to a hard sphere fluid and a spatially random system. We find that the results for the positionally frozen hard sphere Heisenberg system are fairly similar to those previously obtained for the Heisenberg spin fluid and quantitatively agree with the mean field theory estimates. The random system undergoes the ferromagnetic transition at a higher temperature since the lack of core repulsion increases the spin correlations. In this case however the mean field theory overestimates by far the critical temperature.     

Theory of a Heisenberg spin glass

For the quantum mechanical long-range random Heisenberg model we derive mean field equations in analogy to the TAP equations. The complete solution requires a self-consistent calculation of the dynamical local susceptibility. We discuss a variational approximation above and below the critical point.     

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.     

First and second order transition of frustrated Heisenberg spin systems

Starting from the hypothesis of a second order transition we have studied modifications of the original Heisenberg antiferromagnet on a stacked triangular lattice (STA-model) by the Monte Carlo technique. The change is a local constraint restricting the spins at the corners of selected triangles to add up to zero without stopping them from moving freely (STAR-model). We have studied also the closely related dihedral and trihedral models which can be classified as Stiefel models. We have found indications of a first order transition for all three modified models instead of a universal critical behavior. This is in accordance with the renormalization group investigations but disagrees with the Monte Carlo simulations of the original STA-model favoring a new universality class. For the corresponding x-y antiferromagnet studied before, the second order nature of the transition could also not be confirmed. Received 17 May 1999 and Received in final form 30 July 1999     

On the evolution of higher dimensional Heisenberg continuum spin systems

We consider the evolution of a classical Heisenberg ferromagnetic spin chain in its continuum limit in higher spatial dimensions. It is shown that the evolution of a radially symmetric chain could be identified with the motion of a helical space curve as in the linear case. The resulting invariant equations for the curvature (radial energy density) and torsion (related to current density) are shown to be equivalent to a generalized nonlinear Schrödinger equation, similar to the one derived by Ruijgrok and Jurkiewicz recently. Equivalent linear equations as well as special static solutions of point singular type are obtained. Similarity solutions, a class of which belong to Riccati type, are discussed in detail. For general higher dimensions, a potentially useful formulation is presented: Under stereographic projection of the unit sphere of spin, the equation of motion takes a neater form even with the inclusion of anisotropic interactions. Classes of explicit solutions are reported in higher dimensions. Propagating spin waves, static spin waves of point singular nature and of finite energy in some cases are also discussed.     

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.     

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.     

Systematic approach for spin correlations in Heisenberg systems for all temperatures

An exact formula for the spin correlations is derived by a cumulant expansion generalizing the Blume-Hubbard formalism. From this the correlations can be determined in principle to any order with RPA and mode-mode theory as first and second order approximations.     

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.     

Ordering in Heisenberg spin glasses

For five different Heisenberg spin glass systems, torque experiments were performed in applied magnetic fields up to 4 T. The Dzyaloshinski-Moriya random anisotropy strengths, the in-field torque onset temperatures, and the torque relaxation were measured. Critical exponents were estimated independently using a standard protocol. The data are strong evidence for a true spin glass ordered state which survives under high applied magnetic fields; they can be interpreted consistently in terms of a chiral ordering model with replica symmetry breaking as proposed by Kawamura and co-workers.     

Inhomogeneous Heisenberg spin chain and quantum vortex filament as non-holonomically deformed NLS systems

Through the Hasimoto map, various dynamical systems can be mapped to different integrodifferential generalizations of Nonlinear Schrödinger (NLS) family of equations some of which are known to be integrable. Two such continuum limits, corresponding to the inhomogeneous XXX Heisenberg spin chain [J. Phys. C 15, L1305 (1982)] and that of a thin vortex filament moving in a superfluid with drag [Eur. Phys. J. B 86, 275 (2013) 86; Phys. Rev. E 91, 053201 (2015)], are shown to be particular non-holonomic deformations (NHDs) of the standard NLS system involving generalized parameterizations. Crucially, such NHDs of the NLS system are restricted to specific spectral orders that exactly complements NHDs of the original physical systems. The specific non-holonomic constraints associated with these integrodifferential generalizations additionally posses distinct semi-classical signature.     

Excitations in Heisenberg spin glasses

Within the RPA approach forT=0, the excitations of the Heisenberg spin glass system Eu _x Sr_1–x S are studied by numerical methods, using a continued fraction algorithm. Both the density of statesg(E) and also the spectral functionS(q,E) are calculated for systems with (16)³ sites, withx=0.4, 0.5, and 0.6 (spin glass phase), and also forx0.7 (ferromagnetic phase). Forq-vectors within the (1,1,1) plane,S(q,E) shows magnon peaks even in the spin glass phase, over the whole range ofq. However, these peaks are quite broad, and there is considerable intensity at small energies even for largeq, leading to a finite intercept ofg(E) forE0. Over a large temperature range, the specific heat is approximately linear inT forx0.7.     

Excitations in Heisenberg spin glasses

For the Eu _x Sr_1–x S-system in the spin glass regime (x=0.6 and 0.4) the shape functions of the inelastic neutron scattering cross sections at low temperatures are calculated from a numerical study of the imaginary part(q,E) of the dynamic susceptibility at T=0 K. Within the calculation, the continued fraction algorithms of the preceding paper are applied. Additionally, for low temperatures, the spin-autocorrelation function _u (t) is calculated, averaged over all magnetic sitesl. From this quantity, it is also derived, how the (metastable) Edwards-Anderson order parameterq(T) decreases with increasing T, namely (1-const.·T²). Finally, from a numerical study of the inverse participation ratio it is concluded that the spin excitations in the upper half of the energy range covered by the density of states should be localized.Dedicated to Prof. Dr. W. Döring on the occasion of his 70th birthday     

Spinach--a software library for simulation of spin dynamics in large spin systems

We introduce a software library incorporating our recent research into efficient simulation algorithms for large spin systems. Liouville space simulations (including symmetry, relaxation and chemical kinetics) of most liquid-state NMR experiments on 40+ spin systems can now be performed without effort on a desktop workstation. Much progress has also been made with improving the efficiency of ESR, solid state NMR and Spin Chemistry simulations. Spinach is available for download at http://spindynamics.org.     

Surface spin waves in Heisenberg ferromagnet

The existence conditions and the dispersion laws for surface spin waves in Heisenberg ferromagnet are obtained for any orientation of the surface and any exchange constant or anisotropy field in the surface plane. It is shown that purely decaying modes, both of accoustical or optical types, can occur only for surface having special properties of rotational symmetry.     

Theory of spin diffusion in liquid-phase polymer systems

A general theory of spin diffusion in condensed media is constructed by the method of Zwanzig-Mori projection operators using the superpositional approximation to decouple the many-particle correlation functions. The spin diffusion coefficient is expressed in the form D _sp=D _tr+D _f , where D _tr is the contribution associated with translational displacements of the molecules and D _f is the contribution caused by intermolecular flip-flop processes. The expression for D _tr differs from the well-known Kubo-Green formula for the self-diffusion coefficient D _sd in that the integrand contains an additional factor P _f (t), which is the probability of the molecular spins not participating in intermolecular flip-flop transitions over the time t. A microscopic expression is obtained for D _f in the form of a time integral of the intermolecular dipole-dipole dynamic correlation functions. For liquid-phase polymer system with fairly high molecular mass the condition D _sp≫D _sd is satisfied. Zh. éksp. Teor. Fiz. 114, 538–554 (August 1998)     

Fluctuation-dissipation ratio of the Heisenberg spin glass

The fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. The numerically determined FD ratio exhibits a "one-step-like" behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, T(eff) approximately 2T(g), irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Hérisson and Ocio, and with the chirality scenario of the spin-glass transition.