Local spin excitations and Curie temperature of iron

The expression for the Curie temperature of ferromagnetic metals in the mean field approximations is obtained for arbitrary types of exchange interactions. In the framework of local spin density functional approach an exact formula for the effective exchange parameter J₀ is derived. The numerical calculations for ferromagnetic iron illustrate the possibilities of the method.     

Thermodynamics of a quasi-one-dimensional spin system for molecule-based ferrimagnets

A physical picture of electron spin alignments in organic molecule-based ferrimagnets is given from numerical calculations of magnetic specific heat (C) and magnetic susceptibility (χ) as functions of temperature and static magnetic field (B) in terms of an Ising Hamiltonian for an alternating spin chain. The double-peak structure of specific heat appears for different parameter ratios and different magnetic field B, indicating that one peak originates from the ferromagnetic nature and the other from the antiferromagnetic nature. Meanwhile, we study successively the influence of intermolecular and intramolecular interaction on the magnetic susceptibility, showing that the ferromagnetic spin alignment in the alternating molecular chains of biradicals and monoradicals is equivalent to the ferromagnetic alignment of the effective S=1/2 spins. Our results are consistent with those of the Quantum Monte Carlo simulations and the exact diagonalization method and in qualitative agreement with the experimental ones.     

The one-dimensional ANNNI model in a transverse field: analytic and numerical study of effective Hamiltonians

We consider a quantum spin-1/2 Ising chain with competing nearest and next-nearest neighbor interactions in a transverse magnetic field, which is known to be equivalent to the classical two-dimensional ANNNI model. Within a perturbation theory for small transverse field (corresponding to low temperatures in the classical ANNNI model) we derive two effective Hamiltonians: the free model describing free fermions on a fictitious lattice that excludes particular heavy excitations of the original system; and the complete model, which incorporates creation and annihilation of these fermions. Whereas the former possesses only three phases (ferromagnetic, floating and anti phase), the latter contains the full physics of the 2d ANNNI model, including a paramagnetic phase between the ferromagnetic and floating phase and a Kosterlitz-Thouless transition. New analytic results are derived for the free model, e.g. the excitation spectrum that turns out to be non-trivial. Our effective Hamiltonians are defined on a restricted Hilbert space so that exact diagonalization calculations can be done for much larger system sizes. Results from extensive Lanczos calculations for system sizes up to L = 32 are presented confirming the original predictions from Villain and Bak.     

Transfer tensor method in statistical mechanics

We generalize the transfer matrix method to get exact solutions of d-dimensional classical spin lattice models in statistical mechanics.     

Compactification and signature transition in Kaluza-Klein spinor cosmology

We study the classical and quantum cosmology of a 4 + 1-dimensional space-time with a non-zero cosmological constant coupled to a self-interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor R (t) and an internal scale factor a (t) associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self-interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition from a Euclidean to a Lorentzian domain. Such transitions suggest a compactification mechanism for the internal and external scale factors such that a ∼ R⁻¹ in the Lorentzian region. The corresponding quantum cosmology and the ensuing Wheeler-DeWitt equation have exact solutions in the mini-superspace when the spinor field is free, leading to wavepackets undergoing signature change. The question of stabilization of the extra dimension is also discussed.     

Investigation of soliton solutions with different wave structures to the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation

The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials.These solutions are exerted via the new extended FAN sub-equation method.We successfully obtain dark,bright,combined bright-dark,combined dark-singular,periodic,periodic singular,and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems.3D figures are illustrated under an appropriate selection of parameters.The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena.     

Lie Symmetries of Ishimori Equation

The Ishimori equation is one of the most important(2+1)-dimensional integrable models,which is an integrable generalization of(1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.     

Critical exponents of S=1/2 Heisenberg ladders with ferromagnetic interchain interaction in magnetic fields

The critical properties of the S=1/2 Heisenberg two-leg ladders with a ferromagnetic interchain interaction in magnetic fields are investigated by combining the numerical exact diagonalization method and the finite-size-scaling analysis based on conformal field theory.     

Mössbauer Spectra of Noninteracting Single-Domain Ferromagnetic Particles Including Superparamagnetic Relaxation: Simplification of the Multilevel Method

A simple method of calculation of Mössbauer relaxation spectra of single-domain ferromagnetic particle assemblies is developed from Brown's model of coherent rotation of the magnetization utilizing matrix continued fractions to compute the lineshape. The method allows one to obtain a simple analytical formula for the lineshape in the strong relaxation limit, which provides results in agreement with numerical calculations and radically simplifies analysis of the spectra.     

d-Dimensional hubbard model as a (d + 1)-dimensional classical problem

We show an exact equivalence between the partition function of a d-dimensional model of electrons with short range interactions and a (d + 1)-dimensional classical problem. For d = 1 the latter is the combinatorial problem of two coupled arrow-vertex models.     

An h-adaptive mesh method for Boltzmann-BGK/hydrodynamics coupling

We introduce a coupled method for hydrodynamic and kinetic equations on 2-dimensional h-adaptive meshes. We adopt the Euler equations with a fast kinetic solver in the region near thermodynamical equilibrium, while use the Boltzmann-BGK equation in kinetic regions where fluids are far from equilibrium. A buffer zone is created around the kinetic regions, on which a gradually varying numerical flux is adopted. Based on the property of a continuously discretized cut-off function which describes how the flux varies, the coupling will be conservative. In order for the conservative 2-dimensional specularly reflective boundary condition to be implemented conveniently, the discrete Maxwellian is approximated by a high order continuous formula with improved accuracy on a disc instead of on a square domain. The h-adaptive method can work smoothly with a time-split numerical scheme. Through h-adaptation, the cell number is greatly reduced. This method is particularly suitable for problems with hydrodynamics breakdown on only a small part of the whole domain, so that the total efficiency of the algorithm can be greatly improved. Three numerical examples are presented to validate the proposed method and demonstrate its efficiency.     

Performance of a noise barrier within an enclosed space

The present study involved experimental, theoretical, and numerical analyses of the insertion loss provided by rigid noise barriers in an enclosed space. The existing classical diffuse-field theory may be unable to predict the actual sound pressure level distribution and barrier insertion loss for indoor applications. Although predictions made by the ray tracing method at high frequencies are reasonably satisfactory, the method is computer-intensive and time-consuming. We propose a new formula that incorporates the effects of diffraction theory and the reflection of sound between room surfaces. Our results indicate that the present formula provides more realistic and practical predictions of the barrier insertion loss than existing approaches.     

Doubly uniform semiclassical quantization formula for resonances

The radial Schrödinger equation with an effective potential containing a single well and a single barrier is treated with an improved uniform semiclassical method. The improved quantization formula for complex energies (or resonances) contains a correction term that originates from a uniform treatment of the classically forbidden region near the origin in addition to the more familiar uniform treatment of the barrier region. In the present case the origin has a second-order pole, due to the centrifugal barrier potential term, and/or a Coulomb-type singularity, and these terms dominate the region inside the innermost classical turning point.Numerical results for first-order and third-order approximate complex resonance energies are compared with those of a standard (first- and third-order) barrier-uniform semiclassical method and also with those of ‘exact’ numerical computations.The improved quantization formula provides results in significantly better agreement with the exact results as the angular momentum quantum number l approaches zero.     

Heat transport in low-dimensional systems

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard-particle and hard-disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green–Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ diverges with system size L as κ ～ L ^α. For one-dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given.     

Static properties of the one-dimensional planar ferromagnet in an external field

The thermodynamic functions and the correlation length of the classical one-dimensionalX Y model in an external field are calculated by the numerical integration of the transfer matrix equation in both ferro- and antiferromagnetic cases. We show that for a finite but weak magnetic field the low temperature structure of the ferromagnetic partition function consists of a spin-wave part and a factor corresponding to the interaction of topological excitations. The contributions of the soliton like topological objects to the static properties are calculated through a systematic perturbative method. Finally we discuss in detail the regions of validity of different analytical approaches by comparing them with our exact numerical solution.     

Critical behavior of a spherical model with a free surface

Critical phenomena ind-dimensional ferromagnetic spherical models on hypercubic lattices with free surfaces are studied. The surface specific heat and surface susceptibilities are obtained. The exponents characterizing the divergence of these surface quantities at the bulk critical temperature are found to satisfy recently proposed scaling relations. The variation of the susceptibility with distance from the surface is also discussed. The author's recent scaling theory for surface properties is investigated in detail, and found to give an exact representation for the free energy of a three-dimensional spherical model of finite thickness in finite bulk and surface magnetic fields. A scaling form for the surface free energy is derived.     

General linear response formula for non integrable systems obeying the Vlasov equation

Long-range interacting N-particle systems get trapped into long-living out-of-equilibrium stationary states called quasi-stationary states (QSS). We study here the response to a small external perturbation when such systems are settled into a QSS. In the N → ∞ limit the system is described by the Vlasov equation and QSS are mapped into stable stationary solutions of such equation. We consider this problem in the context of a model that has recently attracted considerable attention, the Hamiltonian mean field (HMF) model. For such a model, stationary inhomogeneous and homogeneous states determine an integrable dynamics in the mean-field effective potential and an action-angle transformation allows one to derive an exact linear response formula. However, such a result would be of limited interest if restricted to the integrable case. In this paper, we show how to derive a general linear response formula which does not use integrability as a requirement. The presence of conservation laws (mass, energy, momentum, etc.) and of further Casimir invariants can be imposed a posteriori. We perform an analysis of the infinite time asymptotics of the response formula for a specific observable, the magnetization in the HMF model, as a result of the application of an external magnetic field, for two stationary stable distributions: the Boltzmann-Gibbs equilibrium distribution and the Fermi-Dirac one. When compared with numerical simulations the predictions of the theory are very good away from the transition energy from inhomogeneous to homogeneous states.     

Exact Solutions of (2+1)-Dimensional HNLS Equation

In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation and reduce the (2+1)-dimensional HNLS equation to some (1+1)-dimensional partial differential systems. Finally, many exact travelling solutions of the (2+1)-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.     

Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

In this paper, the Clarkson–Kruskal direct approach is employed to investigate the exact solutions of the2-dimensional rotational Euler equations for the incompressible fluid. The application of the method leads to a system of completely solvable ordinary differential equations. Several special cases are discussed and novel nonlinear exact solutions with respect to variables x and y are obtained. It is of interest to notice that the pressure p is obtained by the second kind of curvilinear integral and the coefficients of the nonlinear solutions are solitary wave type functions like tanh(kt/2)and sech(kt/2) due to the rotational parameter k = 0. Such phenomenon never appear in the classical Euler equations wherein the Coriolis force arising from the gravity and Earth's rotation is ignored. Finally, illustrative numerical figures are attached to show the behaviors that the exact solutions may exhibit.     

Non-perturbative ground-state of a generalized Hubbard model

A generalized Hubbard model with on-site interactionU, inter-site interactionV, and general correlated hopping is studied using a mapping method. An exact solution of the problem of one hole and one doublyoccupied site moving in a ferromagnetic spin background is obtained. The mapping method used is based on mapping the original many-body problem onto an equivalent tight-binding one with impurities in a higher dimensional space.