Spin-3/2 models on the Cayley tree -- optimum ground state approach

We present a class of optimum ground states for spin-3/2 models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal two-point correlation functions.Comment: LaTeX 2e, 8 embedded eps figures, 14 page

Optimum ground states for spin-32\frac{3}{2} chains

We present a set of {\em optimum ground states} for a large class of spin-$\frac{3}{2}$ chains. Such global ground states are simultaneously ground states of the local Hamiltonian, i.e. the nearest neighbour interaction in the present case. They are constructed in the form of a matrix product. We find three types of phases, namely a {\em weak antiferromagnet}, a {\em weak ferromagnet}, and a {\em dimerized antiferromagnet}. The main physical properties of these phases are calculated exactly by using a transfer matrix technique, in particular magnetization and two spin correlations. Depending on the model parameters, they show a surprisingly rich structure.Comment: LaTeX, 22 pages, 6 embedded Postscript figure

Ground state properties of two spin models with exactly known ground states on the square lattice

We introduce a new two-dimensional model with diagonal four spin exchange and an exactly knownground-state. Using variational ansaetze and exact diagonalisation we calculate upper and lower bounds for the critical coupling of the model. Both for this model and for the Shastry-Sutherland model we study periodic systems up to system size 6x6.Comment: to appear in IJMPC 17, 12 pages, 7 figure

Effect of on- and off-ramps in cellular automata models for traffic flow

We present results on the modeling of on- and off-ramps in cellular automata for traffic flow, especially the Nagel-Schreckenberg model. We study two different types of on-ramps that cause qualitatively the same effects. In a certain density regime one observes plateau formation in the fundamental diagram. The plateau value depends on the input-rate of cars at the on-ramp. The on-ramp acts as a local perturbation that separates the system into two regimes: A regime of free flow and another one where only jammed states exist. This phase separation is the reason for the plateau formation and implies a behaviour analogous to that of stationary defects. This analogy allows to perform very fast simulations of complex traffic networks with a large number of on- and off-ramps because one can parametrise on-ramps in an exceedingly easy way.Comment: 11 pages, 9 figures, accepted for publication in Int. J. Mod. Phys.

Triplet superconductivity in a 1D itinerant electron system with transverse spin anisotropy

In this paper we study the ground state phase diagram of a one-dimensional t-J-U model away from half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With increasing ferromagnetic exchange transitions into a ferrometallic and then a spin gapped triplet superconducting phase take place.Comment: 11 pages, 10 figures, accepted for publication in Eur. Phys. J.

Exact trimer ground states on a spin-1 chain

We construct a new spin-1 model on a chain. Its ground state is determined exactly which is three-fold degenerate by breaking translational invariance. Thus we have trimerization. Excited states cannot be obtained exactly, but we determine a few low-lying ones by using trial states, among them solitons

A new cellular automata model for city traffic

We present a new cellular automata model of vehicular traffic in cities by combining ideas borrowed from the Biham-Middleton-Levine (BML) model of city traffic and the Nagel-Schreckenberg (NaSch) model of highway traffic. The model exhibits a dynamical phase transition to a completely jammed phase at a critical density which depends on the time periods of the synchronized signals.Comment: 6 pages, 5 figures, uses Springer Macros 'lncse', to appear in "Traffic and Granular Flow '99: Social, Traffic, and Granular Dynamics" edited by D. Helbing, H. J. Herrmann, M. Schreckenberg, and D. E. Wolf (Springer, Berlin

Exact ground states of quantum spin-2 models on the hexagonal lattice

We construct exact non-trivial ground states of spin-2 quantum antiferromagnets on the hexagonal lattice. Using the optimum ground state approach we determine the ground state in different subspaces of a general spin-2 Hamiltonian consistent with some realistic symmetries. These states, which are not of simple product form, depend on two free parameters and can be shown to be only weakly degenerate. We find ground states with different types of magnetic order, i.e. a weak antiferromagnet with finite sublattice magnetization and a weak ferromagnet with ferrimagnetic order. For the latter it is argued that a quantum phase transition occurs within the solvable subspace.Comment: 7 pages, accepted for publication in Phys. Rev.

Excitations of anisotropic spin-1 chains with matrix product ground state

We investigate a large class of antiferromagnetic spin-1 chains with nearest neighbour interaction and exactly known matrix product ground state. The spectrum of low-lying excitations is calculated numerically by DMRG and exact diagonalisation. Spin liquid behaviour with an excitation gap is observed meeting the Haldane scenario. Further, we compare properties of the anisotropic model with the well-known isotropic AKLT model and use the analytical single mode approximation to obtain a quantitative understanding of the excitation gap. The low-lying excited states can be interpreted in terms of a magnon-like elementary excitation.Comment: 9 pages, 6 figures, accepted for publication in Eur. Phys. J. B, uses svjour.cl