Marshall-Peierls sign rule in frustrated Heisenberg chains

We consider the frustrated antiferromagnetic s=1 Heisenberg quantum spin chain with regard to the Marshall-Peierls sign rule (MPSR). By using exact diagonalization data we investigate the breakdown of the MPSR in dependence on frustration and compare our findings with data for s=1/2. We calculate a critical value of frustration J_2(crit) where the MPSR is violated. The extrapolation of this value to the infinite chain limit holds J_2(crit) approx. 0.016, lower than in the case of s=1/2 (J_2(crit) approx. 0.027). This points to a stronger influence of frustration in the case of s=1. Nevertheless the calculation of the weight of the Ising-states violating the MPSR shows that the MPSR holds approximately even for quite large frustration and may be used for numerical techniques.Comment: 4 pages (Latex), 2 Postscript figures, to be published in acta physica polonica A (European Conference 'Physics of Magnetism 99'

The anisotropic quantum antiferromagnet on the Sierpinski gasket: Ground state and thermodynamics

We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpinski gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to the Sierpinski gasket with N=42. Using this and other methods we calculate ground state energies, spin gap, spin-spin correlations and specific heat data and conclude that the s=1/2 quantum antiferromagnet on the Sierpinski gasket shows a disordered magnetic ground state with a very short correlation length of about 1 and an, albeit very small, spin gap. This conclusion holds for Heisenberg as well a for XY exchange.Comment: LaTeX: 16 pages, 9 figures, 1 tabl

Semi-Deterministic Subspace Selection for Sparse Recursive Projection-Aggregation Decoding of Reed-Muller Codes

Recursive projection aggregation (RPA) decoding as introduced in [1] is a novel decoding algorithm which performs close to the maximum likelihood decoder for short-length Reed-Muller codes. Recently, an extension to RPA decoding, called sparse multi-decoder RPA (SRPA), has been proposed [2]. The SRPA approach makes use of multiple pruned RPA decoders to lower the amount of computations while keeping the performance loss small compared to RPA decoding. However, the use of multiple sparse decoders again increases the computational burden. Therefore, the focus is on the optimization of sparse single-decoder RPA decoding to keep the complexity small. In this paper, a novel method is proposed, to select subsets of subspaces used in the projection and aggregation step of SRPA decoding in order to decrease the decoding error probability on AWGN channels. The proposed method replaces the random selection of subspace subsets with a semi-deterministic selection method based on a figure of merit that evaluates the performance of each subspace. Our simulation results show that the semi-deterministic subspace selection improves the decoding performance up to $0.2\,\text{dB}$ compared to SRPA. At the same time, the complexity of SRPA decoding for RM codes of order $r\geq 3$ is reduced by up to 81% compared to SRPA

Low-lying excitations and thermodynamics of an antiferromagnetic Heisenberg fractal system of a dimension between one and two

We investigate a frustrated Heisenberg spin-1/2 antiferromagnet on a fractal lattice of dimension d=ln3/ln2 (Sierpinski gasket). Calculations were performed using (a) exact diagonalization of all eigenstates and eigenvectors for systems up to N=15 and (b) the Decoupled-Cell Quantum-Monte-Carlo method for systems up to N=366. We present the low-lying spectrum and the specific heat. The specific heat shows a second maximum in the low-temperature region. This behavior is similar to the behavior of the quantum Heisenberg antiferromagnet on a kagome lattice and suggests a disordered ground state and a spin gap in the considered system.Comment: 2 pages, LaTeX, 3 eps figures, to appear in JMM

Anerkennung oder Nicht-Anerkennung - das war die Frage. Indien im deutsch-deutschen Kalten Krieg 1952-1972

Das 1947 unabhängig gewordene Indien ließ seinen Botschafter im Frühjahr 1951 in Bonn akkreditieren, die Bundesrepublik den ihren ein Jahr später in New Delhi. Die indische Regierung lehnte damals einen von Ost-Berlin gewünschten Botschafteraustausch ab, obgleich sie mit anderen kommunistischen Staaten diplomatische Beziehungen aufnahm. Es dauerte zwanzig Jahre, bis die Regierung in New Delhi auch die in Ost–Berlin voll anerkannte

Marshall-Peierls sign rule for excited states of the frustrated J1-J2 Heisenberg antiferromagnet

We present analytical and numerical calculations for some exited states of the frustrated J1-J2 spin-1/2 Heisenberg model for linear chains and square lattices. We consider the lowest eigenstates in the subspaces determined by the eigenvalue M of the spin operator S_total^z. Because of the reduced number of Ising basis states in the subspaces with higher M we are able to diagonalize systems with up to N=144 spins. We find evidence that the Marshall-Peierls sign rule survives for a relatively large frustration parameter J2.Comment: 7 pages, LaTeX, 4 eps figures, to appear in Physica

The J_1-J_2 antiferromagnet with Dzyaloshinskii-Moriya interaction on the square lattice: An exact diagonalization study

We examine the influence of an anisotropic interaction term of Dzyaloshinskii-Moriya (DM) type on the groundstate ordering of the J_1-J_2 spin-1/2-Heisenberg antiferromagnet on the square lattice. For the DM term we consider several symmetries corresponding to different crystal structures. For the pure J_1-J_2 model there are strong indications for a quantum spin liquid in the region of 0.4 < J_2/J_1 < 0.65. We find that a DM interaction influences the breakdown of the conventional antiferromagnetic order by i) shifting the spin liquid region, ii) changing the isotropic character of the groundstate towards anisotropic correlations and iii) creating for certain symmetries a net ferromagnetic moment.Comment: 7 pages, RevTeX, 6 ps-figures, to appear in J. Phys.: Cond. Ma

Development of a Risk Framework for Industry 4.0 in the Context of Sustainability for Established Manufacturers

The concept of “Industry 4.0” is expected to bring a multitude of benefits for industrial value creation. However, the associated risks hamper its implementation and lack a comprehensive overview. In response, the paper proposes a framework of risks in the context of Industry 4.0 that is related to the Triple Bottom Line of sustainability. The framework is developed from a literature review, as well as from 14 in-depth expert interviews. With respect to economic risks, the risks that are associated with high or false investments are outlined, as well as the threatened business models and increased competition from new market entrants. From an ecological perspective, the increased waste and energy consumption, as well as possible ecological risks related to the concept “lot size one”, are described. From a social perspective, the job losses, risks associated with organizational transformation, and employee requalification, as well as internal resistance, are among the aspects that are considered. Additionally, risks can be associated with technical risks, e.g., technical integration, information technology (IT)-related risks such as data security, and legal and political risks, such as for instance unsolved legal clarity in terms of data possession. Conclusively, the paper discusses the framework with the extant literature, proposes managerial and theoretical implications, and suggests avenues for future research