7,426 research outputs found
Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments
We study the distribution of dynamical quantities in various one-dimensional,
disordered models the critical behavior of which is described by an infinite
randomness fixed point. In the {\it disordered contact process}, the quenched
survival probability defined in fixed random environments is
found to show multi-scaling in the critical point, meaning that
, where the (environment and time-dependent)
exponent has a universal limit distribution when . The
limit distribution is determined by the strong disorder renormalization group
method analytically in the end point of a semi-infinite lattice, where it is
found to be exponential, while, in the infinite system, conjectures on its
limiting behaviors for small and large , which are based on numerical
results, are formulated. By the same method, the quenched survival probability
in the problem of {\it random walks in random environments} is also shown to
exhibit multi-scaling with an exponential limit distribution. In addition to
this, the (imaginary-time) spin-spin autocorrelation function of the {\it
random transverse-field Ising chain} is found to have a form similar to that of
survival probability of the contact process at the level of the renormalization
approach. Consequently, a relationship between the corresponding limit
distributions in the two problems can be established. Finally, the distribution
of the spontaneous magnetization in this model is also discussed.Comment: 16 pages, 7 figure
Infinite-disorder critical points of models with stretched exponential interactions
We show that an interaction decaying as a stretched exponential function of
the distance, , is able to alter the universality class of
short-range systems having an infinite-disorder critical point. To do so, we
study the low-energy properties of the random transverse-field Ising chain with
the above form of interaction by a strong-disorder renormalization group (SDRG)
approach. We obtain that the critical behavior of the model is controlled by
infinite-disorder fixed points different from that of the short-range one if
. In this range, the critical exponents calculated analytically by a
simplified SDRG scheme are found to vary with , while, for , the
model belongs to the same universality class as its short-range variant. The
entanglement entropy of a block of size increases logarithmically with
in the critical point but, as opposed to the short-range model, the prefactor
is disorder-dependent in the range . Numerical results obtained by an
improved SDRG scheme are found to be in agreement with the analytical
predictions. The same fixed points are expected to describe the critical
behavior of, among others, the random contact process with stretched
exponentially decaying activation rates.Comment: 16 pages, 3 figure
Critical behavior of models with infinite disorder at a star junction of chains
We study two models having an infinite-disorder critical point --- the zero
temperature random transverse-field Ising model and the random contact process
--- on a star-like network composed of semi-infinite chains connected to a
common central site. By the strong disorder renormalization group method, the
scaling dimension of the local order parameter at the junction is
calculated. It is found to decrease rapidly with the number of arms, but
remains positive for any finite . This means that, in contrast with the pure
transverse-field Ising model, where the transition becomes of first order for
, it remains continuous in the disordered models, although, for not too
small , it is hardly distinguishable from a discontinuous one owing to a
close-to-zero . The scaling behavior of the order parameter in the
Griffiths-McCoy phase is also analyzed.Comment: 14 page
Old institutions, new challenges: the agricultural knowledge system in Hungary
This paper explores and analyses the Hungarian institutional system for the creation and the transfer of knowledge in the fi eld
of agriculture and rural development. We consider the constitution and operation of the Agricultural Knowledge System (AKS)
in Hungary, focussing on the formally organised aspects, and suggest that both the structure and content of the knowledge
needed in the sector have signifi cantly changed during the past decades. These changes, especially in relation to the sustainability
of agriculture, pose signifi cant challenges to traditional AKS institutions, which often have failed to change in line with
the new requirements. Based on a literature review, interviews and a national stakeholder workshop, we offer an analysis of
Hungarian AKS institutions, their co-ordination, co-operation and communication with each other and with Hungarian rurality,
and of the arising issues and problems concerning the creation and the fl ow of knowledge needed for sustainable agriculture.
We also briefl y explore characteristics of emerging bottom-up structures, called LINSAS (learning and innovation networks for
sustainable agriculture), and explore the signifi cance of the fi ndings in this article for the study of AKS in Europe. This article
is based on preliminary results of the SOLINSA research project, supported by the European Union’s Seventh Framework
Programme
Superdiffusion in a class of networks with marginal long-range connections
A class of cubic networks composed of a regular one-dimensional lattice and a
set of long-range links is introduced. Networks parametrized by a positive
integer k are constructed by starting from a one-dimensional lattice and
iteratively connecting each site of degree 2 with a th neighboring site of
degree 2. Specifying the way pairs of sites to be connected are selected,
various random and regular networks are defined, all of which have a power-law
edge-length distribution of the form with the marginal
exponent s=1. In all these networks, lengths of shortest paths grow as a power
of the distance and random walk is super-diffusive. Applying a renormalization
group method, the corresponding shortest-path dimensions and random-walk
dimensions are calculated exactly for k=1 networks and for k=2 regular
networks; in other cases, they are estimated by numerical methods. Although,
s=1 holds for all representatives of this class, the above quantities are found
to depend on the details of the structure of networks controlled by k and other
parameters.Comment: 10 pages, 9 figure
Entanglement across extended random defects in the XX spin chain
We study the half-chain entanglement entropy in the ground state of the
spin-1/2 XX chain across an extended random defect, where the strength of
disorder decays with the distance from the interface algebraically as
. In the whole regime , the average
entanglement entropy is found to increase logarithmically with the system size
as , where the effective
central charge depends on . In the regime
, where the extended defect is a relevant perturbation, the
strong-disorder renormalization group method gives , while, in the regime , where the
extended defect is irrelevant in the bulk, numerical results indicate a
non-zero effective central charge, which increases with . The variation
of is thus found to be non-monotonic and discontinuous at
.Comment: 16 pages, 8 figure
Defining and classifying TQFTs via surgery
We give a presentation of the -dimensional oriented cobordism category
with generators corresponding to diffeomorphisms and surgeries
along framed spheres, and a complete set of relations. Hence, given a functor
from the category of smooth oriented manifolds and diffeomorphisms to an
arbitrary category , and morphisms induced by surgeries along framed
spheres, we obtain a necessary and sufficient set of relations these have to
satisfy to extend to a functor from to . If is symmetric
and monoidal, then we also characterize when the extension is a TQFT.
This framework is well-suited to defining natural cobordism maps in Heegaard
Floer homology. It also allows us to give a short proof of the classical
correspondence between (1+1)-dimensional TQFTs and commutative Frobenius
algebras. Finally, we use it to classify (2+1)-dimensional TQFTs in terms of
J-algebras, a new algebraic structure that consists of a split graded
involutive nearly Frobenius algebra endowed with a certain mapping class group
representation. This solves a long-standing open problem. As a corollary, we
obtain a structure theorem for (2+1)-dimensional TQFTs that assign a vector
space of the same dimension to every connected surface. We also note that there
are nonequivalent lax monoidal TQFTs over that do
not extend to (1+1+1)-dimensional ones.Comment: 68 pages, 4 figures, to appear in Quantum Topolog
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