20 research outputs found
A Spin - 3/2 Ising Model on a Square Lattice
The spin - 3/2 Ising model on a square lattice is investigated. It is shown
that this model is reducible to an eight - vertex model on a surface in the
parameter space spanned by coupling constants J, K, L and M. It is shown that
this model is equivalent to an exactly solvable free fermion model along two
lines in the parameter space.Comment: LaTeX, 7 pages, 1 figure upon request; JETP Letters, in pres
Exact correlation functions of Bethe lattice spin models in external fields
We develop a transfer matrix method to compute exactly the spin-spin
correlation functions of Bethe lattice spin models in the external magnetic
field h and for any temperature T. We first compute the correlation function
for the most general spin - S Ising model, which contains all possible
single-ion and nearest-neighbor pair interactions. This general spin - S Ising
model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths
(BEG) model as special cases. From the spin-spin correlation functions, we
obtain functions of correlation length for the simple Ising model and BEG
model, which show interesting scaling and divergent behavior as T approaches
the critical temperature. Our method to compute exact spin-spin correlation
functions may be applied to other Ising-type models on Bethe and Bethe-like
lattices.Comment: 19 page
Quantum computation based on d-level cluster states
The concept of qudit (a d-level system) cluster state is proposed by
generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001))
according to the finite dimensional representations of quantum plane algebra.
We demonstrate their quantum correlations and prove a theorem which guarantees
the availability of the qudit cluster states in quantum computation. We
explicitly construct the network to show the universality of the one-way
computer based on the defined qudit cluster states and single-qudit
measurement. And the corresponding protocol of implementing one-way quantum
computer can be suggested with the high dimensional "Ising" model which can be
found in many magnetic systems.Comment: Revtex4, 15 pages, 3 eps figure
3-cocycles, non-associative star-products and the magnetic paradigm of R-flux string vacua
We consider the geometric and non-geometric faces of closed string vacua arising by T-duality from principal torus bundles with constant H-flux and pay attention to their double phase space description encompassing all toroidal coordinates, momenta and their dual on equal footing. We construct a star-product algebra on functions in phase space that is manifestly duality invariant and substitutes for canonical quantization. The 3-cocycles of the Abelian group of translations in double phase space are seen to account for non-associativity of the star-product. We also provide alternative cohomological descriptions of non-associativity and draw analogies with the quantization of point-particles in the field of a Dirac monopole or other distributions of magnetic charge. The magnetic field analogue of the R-flux string model is provided by a constant uniform distribution of magnetic charge in space and non-associativity manifests as breaking of angular symmetry. The Poincare vector comes to rescue angular symmetry as well as associativity and also allow for quantization in terms of operators and Hilbert space only in the case of charged particles moving in the field of a single magnetic monopole