187 research outputs found
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- chains
We present a set of {\em optimum ground states} for a large class of
spin- 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
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
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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.
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