Spin chains with nearest and next nearest neighbour interactions

The 1/n-expansion is applied to a classical one dimensionaln-vector model in an external field with nearest and next nearest neighbour exchange interactions of both signs. Various effects caused by helical spin structures are discussed for the Heisenberg magnet (n=3).—For the spherical model with multi-neighbour interactions Lifshitz points of higher order are found.     

The spin-peierls critical temperature in an XY quasi-one-dimensional system with nearest and next-nearest neighbour interactions

The mean field critical temperature for the spin-Peierls phase transition in the XY antiferromagnetic chain is obtained for nearest and next nearest neighbour exchange interaction. An increase in T_c is predicted for next nearest neighbour antiferromagnetic exchange and a decrease is obtained for ferromagnetic exchange. This model is applied to the alkali-TCNQ salts, which are treated in the framework of the highly correlated Hubbard model.     

Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point . We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.     

A chiral axial next nearest neighbour xy-model for antiferroelectric liquid crystals

We describe a chiral axial next nearest neighbour xy-model to account for the various subphases exhibited by antiferroelectric liquid crystals made of chiral rod-like molecules. The assumed form of the interlayer interactions is based on physical processes which are discussed. Using a discrete model, the predicted sequence of transitions is SmA-SmC-SmC-FI_H-FI_I-FI_L-SmC ^* A, where FI stands for a ferriphase, as seen in many compounds. The ferri and SmC phases are characterized by relatively large angles between the c-vectors of successive layers and occur only when the compounds have high optical purity. The calculated field induced structures exhibit a plateau of the apparent tilt angle at , where is the tilt angle of the molecules in the ferriphase. The conoscopic figures in the presence of a field and ellipsometric parameters in the absence of a field have also been generated, which agree extremely well with the experimental results. Recent anomalous X-ray scattering studies prove the xy-character of the configurations, though the commensurate structures that are found in the ferriphase require an extension of the model to include lock-in terms. Received 23 August 1999     

Exact groundstates for antiferromagnetic spin-one chains with nearest and next-nearest neighbour interactions

We have found the exact ground state for a large class of antiferromagnetic spin-one chains with nearest and next-nearest neighbour interactions. The ground state is characterized as a matrix product of local site states and has the properties characteristic of the Haldane scenario.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Percolation with nearest neighbour interaction

A Monte Carlo technique is used to investigate site percolation in a three dimensional lattice in which the presence of occupied sites influences the selection of the next site for occupation. Results are given for a simple cubic geometry.     

Nonlinear diffusion limit for a system with nearest neighbor interactions

We consider a system of interacting diffusions. The variables are to be thought of as charges at sites indexed by a periodic one-dimensional lattice. The diffusion preserves the total charge and the interaction is of nearest neighbor type. With the appropriate scaling of lattice spacing and time, a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density.Work supported by the National Science Foundation under grants no. DMS 8600233 and DMS 8701895     

Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm

In this article we study the classical nearest-neighbour spin-ice model (nnSI) by means of Monte Carlo simulations, using the Wang-Landau algorithm. The nnSI describes several of the salient features of the spin-ice materials. Despite its simplicity it exhibits a remarkably rich behaviour. The model has been studied using a variety of techniques, thus it serves as an ideal benchmark to test the capabilities of the Wang Landau algorithm in magnetically frustrated systems. We study in detail the residual entropy of the nnSI and, by introducing an applied magnetic field in two different crystallographic directions ([111] and [100]), we explore the physics of the kagome-ice phase, the transition to full polarisation, and the three dimensional Kasteleyn transition. In the latter case, we discuss how additional constraints can be added to the Hamiltonian, by taking into account a selective choice of states in the partition function and, then, show how this choice leads to the realization of the ideal Kasteleyn transition in the system.     

ESR of a Mn-S nearest neighbour complex in GaP

ESR measurements on a manganese-sulphur nearest neighbour complex having axial symmetry along 〈111〉 axes are reported. The spin Hamiltonian parameters are found to be g = 2.002 ± 0.001, A = (-57 ±1) × 10^-4 cm^-1, D = (-306 ± 2) × 10^-4 cm^-1 and (a − F) = (+12 ±2) × 10^-4 cm^-1. The formation of these complexes is discussed. briefly.     

长程作用下Gauss系统的临界温度

利用傅里叶变换的方法，严格求解了d维(d=1，2和3)超立方晶格和二维三角晶格上具有长程 相互作用的Gauss模型(这里考虑的长程作用有幂指数、指数和对数三种形式).得到了这些情 况下系统的临界点(温度)，并对不同形式的长程作用对临界点的影响进行了比较.结果表明 ，长程相互作用的存在，使得系统的临界温度有了一定程度的升高，它们对系统临界温度的 影响与其衰减的快慢有关. 关键词： Gauss模型 临界点 超立方晶格 三角晶格     

Exact value of the ground state energy of the linear antiferromagnetic Heisenberg chain with nearest and next-nearest neighbour interactions

It is shown that the ground state energy of the hamiltonian $\text{H = Σ}\text{S}{}_{\mathrm{i}}\text{·}\text{S}{}_{\mathrm{i+1}}\text{+ γΣ}\text{S}{}_{\mathrm{i}}\text{·}\text{S}{}_{\mathrm{i+2}}$ for the linear antiferromagnetic Heisenberg chain with nearest and next-nearest neighbour interactions is equal to $\text{-}\text{3}\text{2}\text{if}\text{γ =}\text{1}\text{2}$.     

An exact analytic treatment of an ordered binary alloy in a Bethe lattice including first and second nearest neighbour interactions

Exact analytic formulae are obtained for the electronic structure of an ordered binary alloy in a Bethe lattice described by a tight-binding hamiltonian that includes nearest neighbour and second nearest neighbour interactions. Some interesting results are obtained and discussed in the text.     

Degeneracy of solitons and polarons in polyacetylene for translation between nearest neighbour sites

In polyacetylene, there are solitons with two different interface natures, one connecting oppositely dimerized chains by two single bonds and another by two double bonds. There are also polarons of two kinds, one with the center on a double bond and another on a single bond. These two kinds of solitons and polarons are converted to each other by translation between nearest neighbour sites. They have apparently different electronic structures but are degenerate in energy and have the same lattice structure. The origin of the degeneracy is disclosed.     

Phase transition in a linear chain of classical spins with a logarithmic nearest neighbour pair potential

We present the complete calculation of the partition function and correlation functions of a linear array of classical spins coupled by a nearest neighbour logarithmic pair potential. In the case of a ferromagnetic coupling there occurs a phase transition at T_c > 0. The critical exponents of the specific heat C and the magnetic susceptibility χ (in the absence of an external field) are shown to have the non-classical value α = 2 and classical value γ = 1 respectively. The underlying mathematical mechanism of the phase transition is the complete degeneracy of all the eigenvalues of the corresponding integral equation (Kac's mechanism). Below T_c the partition function becomes complex. For antiferromagnetic coupling the free energy is analytic in the whole temperature range and so no phase transition occurs in this case.     

Impurity pair modes in a diatomic linear chain: nearest neighbour pair

The behaviour of the impurity modes due to a pair of substitutional impurities characterized by both mass as well as force-constant changes and occupying nearest neighbour positions in a diatomic linear chain, is studied. The results are compared with those for the case of impurity pairs occupying next nearest neighbour sites discussed earlier as well as the existing three dimensional calculations of Elliott and Pfeuty. The nearest neighbour impurity pair gap and local modes can be interpreted in terms of two single impurities substituted in the two different sublattices unlike the next nearest neighbour pair modes. The inband resonant modes are totally new features characteristic of the pair. Finally, the predictions of the theory are compared with the available experimental data for Si-impurity-pair-complexes and qualitative agreement is shown.     

Critical relaxation for spin system with long range interactions

The relaxation rates for time independent spin correlation functions are estimated for a long range interaction. The damping of a critical spin variable in the critical region is found to be a function of this range.     

Spin orderings of the one-dimensional Ising magnet with the nearest and next nearest neighbor interaction

A proof is given of the fact that there exist four possible spin orderings for the one-dimensional Ising magnet with nearest and next-nearest-neighbor interactions.     

Brillouin zone unfolding of complex bands in a nearest neighbour tight binding scheme

Complex bands k(⊥)(E) in a semiconductor crystal, along a general direction n, can be computed by casting Schr?dinger's equation as a generalized polynomial eigenvalue problem. When working with primitive lattice vectors, the order of this eigenvalue problem can grow large for arbitrary n. It is, however, possible to always choose a set of non-primitive lattice vectors such that the eigenvalue problem is restricted to be quadratic. The complex bands so obtained need to be unfolded onto the primitive Brillouin zone. In this paper, we present a unified method to unfold real and complex bands. Our method ensures that the measure associated with the projections of the non-primary wavefunction onto all candidate primary wavefunctions is invariant with respect to the energy E.     

The first and second nearest neighbour Cr3+ pairs in ruby

The irreducible representations of the states of the first and second nearest neighbour Cr³⁺ pairs in ruby were deduced from the known states of the single ions by the group theoretical method of induction. The summetry selection rules and polarizations for electric dipole radiation are discussed.Supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 65 Frankfurt-Darmstadt.