1,768 research outputs found
The Heisenberg antiferromagnet on a triangular lattice: topological excitations
We study the topological defects in the classical Heisenberg antiferromagnet
in two dimensions on a triangular lattice (HAFT). While the topological
analysis of the order parameter space indicates that the defects are of
type, consideration of the energy leads us to a description of the low--energy
stationary points of the action in terms of vortices, as in the planar XY
model. Starting with the continuum description of the HAFT, we show
analytically that its partition function can be reduced to that of a
2--dimensional Coulomb gas with logarithmic interaction. Thus, at low
temperatures, the correlation length is determined by the spinwaves, while at
higher temperatures we expect a crossover to a Kosterlitz--Thouless type
behaviour. The results of recent Monte Carlo calculations of the correlation
length are consistent with such a crossover.Comment: 9 pages, revtex, preprint: ITP-UH 03/9
Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations
We have simulated the classical Heisenberg antiferromagnet on a triangular
lattice using a local Monte Carlo algorithm. The behavior of the correlation
length , the susceptibility at the ordering wavevector , and
the spin stiffness clearly reflects the existence of two temperature
regimes -- a high temperature regime , in which the disordering
effect of vortices is dominant, and a low temperature regime ,
where correlations are controlled by small amplitude spin fluctuations. As has
previously been shown, in the last regime, the behavior of the above quantities
agrees well with the predictions of a renormalization group treatment of the
appropriate nonlinear sigma model. For , a satisfactory fit of the
data is achieved, if the temperature dependence of and is
assumed to be of the form predicted by the Kosterlitz--Thouless theory.
Surprisingly, the crossover between the two regimes appears to happen in a very
narrow temperature interval around .Comment: 13 pages, 8 Postscript figure
Correlations in the Ising antiferromagnet on the anisotropic kagome lattice
We study the correlation function of middle spins, i. e. of spins on
intermediate sites between two adjacent parallel lattice axes, of the spatially
anisotropic Ising antiferromagnet on the kagome lattice. It is given rigorously
by a Toeplitz determinant. The large-distance behaviour of this correlation
function is obtained by analytic methods. For shorter distances we evaluate the
Toeplitz determinant numerically. The correlation function is found to vanish
exactly on a line J_d(T) in the T-J (temperature vs. coupling constant) phase
diagram. This disorder line divides the phase diagram into two regions. For J
less than J_d(T) the correlations display the features of an unfrustrated
two-dimensional Ising magnet, whereas for J greater than J_d(T) the
correlations between the middle spins are seen to be strongly influenced by the
short-range antiferromagnetic order that prevails among the spins of the
adjacent lattice axes. While for J less than J_d(T) there is a region with
ferrimagnetic long-range order, the model remains disordered for J greater than
J_d(T) down to T=0.Comment: 26 pages, 9 figures, published versio
From Tomonaga-Luttinger to Fermi liquid in transport through a tunneling barrier
Finite length of a one channel wire results in crossover from a
Tomonaga-Luttinger to Fermi liquid behavior with lowering energy scale. In
condition that voltage drop mostly occurs across a tunnel barrier inside
the wire we found coefficients of temperature/voltage expansion of low energy
conductance as a function of constant of interaction, right and left traversal
times. At higher voltage the finite length contribution exhibits oscillations
related to both traversal times and becomes a slowly decaying correction to the
scale-invariant dependence of the conductance.Comment: 12 pages of RevTex file and 1 PS file figur
Anderson-localization versus delocalization of interacting fermions in one dimension
Using the density matrix renormalization group algorithm, we investigate the
lattice model for spinless fermions in one dimension in the presence of a
strong interaction and disorder. The phase sensitivity of the ground state
energy is determined with high accuracy for systems up to a size of 60 lattice
constants. This quantity is found to be log-normally distributed. The
fluctuations grow algebraically with system size with a universal exponent of
~2/3 in the localized region of the phase diagram. Surprizingly, we find, for
an attractive interaction, a delocalized phase of finite extension. The
boundary of this delocalized phase is determined.Comment: 5 pages, 6 figures, revte
Scaling behavior of impurities in mesoscopic Luttinger liquids
Using a functional renormalization group we compute the flow of the
renormalized impurity potential for a single impurity in a Luttinger liquid
over the entire energy range - from the microscopic scale of a lattice-fermion
model down to the low-energy limit. The non-perturbative method provides a
complete real-space picture of the effective impurity potential. We confirm the
universality of the open chain fixed point, but it turns out that very large
systems (10^4-10^5 sites) are required to reach the fixed point for realistic
choices of the impurity and interaction parameters.Comment: 4 pages, 4 figures include
Persistent currents in mesoscopic rings: A numerical and renormalization group study
The persistent current in a lattice model of a one-dimensional interacting
electron system is systematically studied using a complex version of the
density matrix renormalization group algorithm and the functional
renormalization group method. We mainly focus on the situation where a single
impurity is included in the ring penetrated by a magnetic flux. Due to the
interplay of the electron-electron interaction and the impurity the persistent
current in a system of N lattice sites vanishes faster then 1/N. Only for very
large systems and large impurities our results are consistent with the
bosonization prediction obtained for an effective field theory. The results
from the density matrix renormalization group and the functional
renormalization group agree well for interactions as large as the band width,
even though as an approximation in the latter method the flow of the
two-particle vertex is neglected. This confirms that the functional
renormalization group method is a very powerful tool to investigate correlated
electron systems. The method will become very useful for the theoretical
description of the electronic properties of small conducting ring molecules.Comment: 9 pages, 8 figures include
On the Dialectics of Global Governance in the Twenty-first Century : A Polanyian Double Movement?
Following decades of economic globalisation and market-oriented reforms across the world, Karl Polanyi’s double movement has been invoked not only to explain what is happening but also to give reasons for being hopeful about a different future. Some have suggested a pendulum model of history: a swing from markets to society leading, in the next phase, to a swing from society to markets, and so on. The double movement can also be understood dialectically as a description of an irreversible historical development following its own inner laws or schemes of development. Going beyond a thesis – antithesis – synthesis pattern, I maintain that conceptions and schemes drawn from dialectics, and especially dialectical critical realism, can provide better geo-historical hypotheses for explaining past changes and for building scenarios about possible future changes. I analyse political economy contradictions and tendencies, and focus on normative rationality, to assess substantial claims about rational tendential directionality of world history. I argue that democratic global Keynesianism would enable processes of decommodification and new syntheses concerning the market/social nexus. A learning process towards qualitatively higher levels of reflexivity can help develop global transformative agency. Existing contradictions can be resolved by means of rational collective actions and building more adequate common institutions. These collective actions are likely to involve new forms of political agency such as world political parties.Peer reviewe
Quantum Monte Carlo simulation for the conductance of one-dimensional quantum spin systems
Recently, the stochastic series expansion (SSE) has been proposed as a
powerful MC-method, which allows simulations at low for quantum-spin
systems. We show that the SSE allows to compute the magnetic conductance for
various one-dimensional spin systems without further approximations. We
consider various modifications of the anisotropic Heisenberg chain. We recover
the Kane-Fisher scaling for one impurity in a Luttinger-liquid and study the
influence of non-interacting leads for the conductance of an interacting
system.Comment: 8 pages, 9 figure
Electronic Spectral Functions for Quantum Hall Edge States
We have evaluated wavevector-dependent electronic spectral functions for
integer and fractional quantum Hall edge states using a chiral Luttinger liquid
model. The spectral functions have a finite width and a complicated line shape
because of the long-range of the Coulomb interaction. We discuss the
possibility of probing these line shapes in vertical tunneling experiments.Comment: 4 pages, RevTex, two figures included, to appear as a Rapid
Communication in PRB; we updated references which have recently appeared in
print and were cited as preprints in our ealier submissio
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