61,467 research outputs found
High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets
The ground states of Klein type spin models on the pyrochlore and
checkerboard lattice are spanned by the set of singlet dimer coverings, and
thus possess an extensive ground--state degeneracy. Among the many exotic
consequences is the presence of deconfined fractional excitations (spinons)
which propagate through the entire system. While a realistic electronic model
on the pyrochlore lattice is close to the Klein point, this point is in fact
inherently unstable because any perturbation restores spinon
confinement at . We demonstrate that deconfinement is recovered in the
finite--temperature region , where the deconfined phase
can be characterized as a dilute Coulomb gas of thermally excited spinons. We
investigate the zero--temperature phase diagram away from the Klein point by
means of a variational approach based on the singlet dimer coverings of the
pyrochlore lattices and taking into account their non--orthogonality. We find
that in these systems, nearest neighbor exchange interactions do not lead to
Rokhsar-Kivelson type processes.Comment: 19 page
Frameworks, Symmetry and Rigidity
Symmetry equations are obtained for the rigidity matrix of a bar-joint
framework in R^d. These form the basis for a short proof of the Fowler-Guest
symmetry group generalisation of the Calladine-Maxwell counting rules. Similar
symmetry equations are obtained for the Jacobian of diverse framework systems,
including constrained point-line systems that appear in CAD, body-pin
frameworks, hybrid systems of distance constrained objects and infinite
bar-joint frameworks. This leads to generalised forms of the Fowler-Guest
character formula together with counting rules in terms of counts of
symmetry-fixed elements. Necessary conditions for isostaticity are obtained for
asymmetric frameworks, both when symmetries are present in subframeworks and
when symmetries occur in partition-derived frameworks.Comment: 5 Figures. Replaces Dec. 2008 version. To appear in IJCG
Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model
The dynamical behaviours of a kinetically constrained spin model
(Fredrickson-Andersen model) on a Bethe lattice are investigated by a
perturbation analysis that provides exact final states above the nonergodic
transition point. It is observed that the time-dependent solutions of the
derived dynamical systems obtained by the perturbation analysis become
systematically closer to the results obtained by Monte Carlo simulations as the
order of a perturbation series is increased. This systematic perturbation
analysis also clarifies the existence of a dynamical scaling law, which
provides a implication for a universal relation between a size scale and a time
scale near the nonergodic transition.Comment: 17 pages, 7 figures, v2; results have been refined, v3; A figure has
been modified, v4; results have been more refine
The Axelrod model for the dissemination of culture revisited
This article is concerned with the Axelrod model, a stochastic process which
similarly to the voter model includes social influence, but unlike the voter
model also accounts for homophily. Each vertex of the network of interactions
is characterized by a set of cultural features, each of which can assume
states. Pairs of adjacent vertices interact at a rate proportional to the
number of features they share, which results in the interacting pair having one
more cultural feature in common. The Axelrod model has been extensively studied
during the past ten years, based on numerical simulations and simple mean-field
treatments, while there is a total lack of analytical results for the spatial
model itself. Simulation results for the one-dimensional system led physicists
to formulate the following conjectures. When the number of features and the
number of states both equal two, or when the number of features exceeds the
number of states, the system converges to a monocultural equilibrium in the
sense that the number of cultural domains rescaled by the population size
converges to zero as the population goes to infinity. In contrast, when the
number of states exceeds the number of features, the system freezes in a highly
fragmented configuration in which the ultimate number of cultural domains
scales like the population size. In this article, we prove analytically for the
one-dimensional system convergence to a monocultural equilibrium in terms of
clustering when , as well as fixation to a highly fragmented
configuration when the number of states is sufficiently larger than the number
of features. Our first result also implies clustering of the one-dimensional
constrained voter model.Comment: Published in at http://dx.doi.org/10.1214/11-AAP790 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Statistical equilibrium of tetrahedra from maximum entropy principle
Discrete formulations of (quantum) gravity in four spacetime dimensions build
space out of tetrahedra. We investigate a statistical mechanical system of
tetrahedra from a many-body point of view based on non-local, combinatorial
gluing constraints that are modelled as multi-particle interactions. We focus
on Gibbs equilibrium states, constructed using Jaynes' principle of constrained
maximisation of entropy, which has been shown recently to play an important
role in characterising equilibrium in background independent systems. We apply
this principle first to classical systems of many tetrahedra using different
examples of geometrically motivated constraints. Then for a system of quantum
tetrahedra, we show that the quantum statistical partition function of a Gibbs
state with respect to some constraint operator can be reinterpreted as a
partition function for a quantum field theory of tetrahedra, taking the form of
a group field theory.Comment: v3 published version; v2 18 pages, 4 figures, improved text in
sections IIIC & IVB, minor changes elsewher
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