25 research outputs found
A Spin-1/2 Model for CsCuCl_3 in an External Magnetic Field
CsCuCl_3 is a ferromagnetically stacked triangular spin-1/2 antiferromagnet.
We discuss models for its zero-temperature magnetization process. The models
range from three antiferromagnetically coupled ferromagnetic chains to the full
three-dimensional situation. The situation with spin-1/2 is treated by
expansions around the Ising limit and exact diagonalization. Further,
weak-coupling perturbation theory is used mainly for three coupled chains which
are also investigated numerically using the density-matrix renormalization
group technique. We find that already the three-chain model gives rise to the
plateau-like feature at one third of the saturation magnetization which is
observed in magnetization experiments on CsCuCl_3 for a magnetic field
perpendicular to the crystal axis. For a magnetic field parallel to the crystal
axis, a jump is observed in the experimental magnetization curve in the region
of again about one third of the saturation magnetization. In contrast to
earlier spinwave computations, we do not find any evidence for such a jump with
the model in the appropriate parameter region.Comment: 13 pages LaTeX2e with EPJ macro package (included), 8 (e)ps figures
included using psfig.sty; this is the final version to appear in Eur. Phys. J
B; a few further explanations and one reference adde
Ising films with surface defects
The influence of surface defects on the critical properties of magnetic films
is studied for Ising models with nearest-neighbour ferromagnetic couplings. The
defects include one or two adjacent lines of additional atoms and a step on the
surface. For the calculations, both density-matrix renormalization group and
Monte Carlo techniques are used. By changing the local couplings at the defects
and the film thickness, non-universal features as well as interesting crossover
phenomena in the magnetic exponents are observed.Comment: 8 pages, 12 figures included, submitted to European Physical Journal
Ising thin films with modulations and surface defects
Properties of magnetic films are studied in the framework of Ising models. In
particular, we discuss critical phenomena of ferromagnetic Ising films with
straight lines of magnetic adatoms and straight steps on the surface as well as
phase diagrams of the axial next-nearest neighbour Ising (ANNNI) model for thin
films exhibiting various spatially modulated phases.Comment: 6 pages, 4 figures include
The generalized contact process with n absorbing states
We investigate the critical properties of a one dimensional stochastic
lattice model with n (permutation symmetric) absorbing states. We analyze the
cases with by means of the non-hermitian density matrix
renormalization group. For n=1 and n=2 we find that the model is respectively
in the directed percolation and parity conserving universality class,
consistent with previous studies. For n=3 and n=4, the model is in the active
phase in the whole parameter space and the critical point is shifted to the
limit of one infinite reaction rate. We show that in this limit the dynamics of
the model can be mapped onto that of a zero temperature n-state Potts model. On
the basis of our numerical and analytical results we conjecture that the model
is in the same universality class for all with exponents , and . These exponents
coincide with those of the multispecies (bosonic) branching annihilating random
walks. For n=3 we also show that, upon breaking the symmetry to a lower one
(), one gets a transition either in the directed percolation, or in the
parity conserving class, depending on the choice of parameters.Comment: 10 pages, RevTeX, and 10 PostScript figures include
Density-Matrix Spectra of Solvable Fermionic Systems
We consider non-interacting fermions on a lattice and give a general result
for the reduced density matrices corresponding to parts of the system. This
allows to calculate their spectra, which are essential in the DMRG method, by
diagonalizing small matrices. We discuss these spectra and their typical
features for various fermionic quantum chains and for the two-dimensional
tight-binding model.Comment: 12 pages and 9 figure
Construction of a matrix product stationary state from solutions of finite size system
Stationary states of stochastic models, which have states per site, in
matrix product form are considered. First we give a necessary condition for the
existence of a finite -dimensional matrix product state for any .
Second, we give a method to construct the matrices from the stationary states
of small size system when the above condition and are satisfied.
Third, the method by which one can check that the obtained matrices are valid
for any system size is presented for the case where is satisfied. The
application of our methods is explained using three examples: the asymmetric
exclusion process, a model studied in [F. H. Jafarpour: J. Phys. A: Math. Gen.
36 (2003) 7497] and a hybrid of both of the models.Comment: 22 pages, no figure. Major changes: sec.3 was shortened; the list of
references were changed. This is the final version, which will appear in
J.Phys.
The one-dimensional contact process: duality and renormalisation
We study the one-dimensional contact process in its quantum version using a
recently proposed real space renormalisation technique for stochastic
many-particle systems. Exploiting the duality and other properties of the
model, we can apply the method for cells with up to 37 sites. After suitable
extrapolation, we obtain exponent estimates which are comparable in accuracy
with the best known in the literature.Comment: 15 page
The non-equilibrium phase transition of the pair-contact process with diffusion
The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles
is a simple branching-annihilation processes which exhibits a phase transition
from an active into an absorbing phase with an unusual type of critical
behaviour which had not been seen before. Although the model has attracted
considerable interest during the past few years it is not yet clear how its
critical behaviour can be characterized and to what extent the diffusive
pair-contact process represents an independent universality class. Recent
research is reviewed and some standing open questions are outlined.Comment: Latexe2e, 53 pp, with IOP macros, some details adde
Density-Matrix Renormalization-Group Analysis of Quantum Critical Points: I. Quantum Spin Chains
We present a simple method, combining the density-matrix
renormalization-group (DMRG) algorithm with finite-size scaling, which permits
the study of critical behavior in quantum spin chains. Spin moments and
dimerization are induced by boundary conditions at the chain ends and these
exhibit power-law decay at critical points. Results are presented for the
spin-1/2 Heisenberg antiferromagnet; an analytic calculation shows that
logarithmic corrections to scaling can sometimes be avoided. We also examine
the spin-1 chain at the critical point separating the Haldane gap and dimerized
phases. Exponents for the dimer-dimer and the spin-spin correlation functions
are consistent with results obtained from bosonization.Comment: 21 pages, 12 figures, new results and added references, to appear in
PR
Entanglement in solvable many-particle models
Lecture notes for the Brazilian School on Statistical Mechanics, Natal,
Brazil, July 2011.
The five lectures introduce to the description of entanglement in
many-particle systems and review the ground-state entanglement features of
standard solvable lattice models. This is done using a thermodynamic
formulation in which the eigenvalue spectrum of a certain Hamiltonian
determines the entanglement properties. The methods to obtain it are discussed
and results, both analytical and numerical, for various cases including time
evolution are presented.Comment: 44 pages, 30 figures. Lecture notes for the Brazilian School on
Statistical Mechanics, Natal, July 2011. For the Brazilian Journal of Physic