847 research outputs found
An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
We introduce a spin chain based on finite-dimensional spin-1/2 SU(2)
representations but with a non-hermitian `Hamiltonian' and show, using mostly
analytical techniques, that it is described at low energies by the SL(2,R)/U(1)
Euclidian black hole Conformal Field Theory. This identification goes beyond
the appearance of a non-compact spectrum: we are also able to determine the
density of states, and show that it agrees with the formulas in [J. Math. Phys.
42, 2961 (2001)] and [JHEP 04, 014 (2002)], hence providing a direct `physical
measurement' of the associated reflection amplitude.Comment: 6 pages, 3 figures, in RevTeX. Corrected some typo
GPs’ strategies in exploring the preschool child’s wellbeing in the paediatric consultation
Background:
Although General Practitioners (GPs) are uniquely placed to identify children with emotional, social, and behavioural problems, they succeed in identifying only a small number of them. The aim of this article is to explore the strategies, methods, and tools employed by GPs in the assessment of the preschool child’s emotional, mental, social, and behavioural health. We look at how GPs address parental care of the child in general and in situations where GPs have a particular awareness of the child.
Method:
Twenty-eight Danish GPs were purposively selected to take part in a qualitative study which combined focus-group discussions, observation of child consultations, and individual interviews with GPs.
Results:
Analysis of the data suggests that GPs have developed a set of methods, and strategies to assess the preschool child and parental care of the child. They look beyond paying narrow attention to the physical health of the child and they have expanded their practice to include the relations and interactions in the consultation room. The physical examination of the child continues to play a central role in doctor-child communication.
Conclusion:
The participating GPs’ strategies helped them to assess the wellbeing of the preschool child but they often find it difficult to share their impressions with parents
Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
The two-dimensional Potts model can be studied either in terms of the
original Q-component spins, or in the geometrical reformulation via
Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for
arbitrary real values of Q by construction, it was only shown very recently
that the spin representation can be promoted to the same level of generality.
In this paper we show how to define the Potts model in terms of observables
that simultaneously keep track of the spin and FK degrees of freedom. This is
first done algebraically in terms of a transfer matrix that couples three
different representations of a partition algebra. Using this, one can study
correlation functions involving any given number of propagating spin clusters
with prescribed colours, each of which contains any given number of distinct FK
clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the
Kac form h_{r,s}, with integer indices r,s that we determine exactly both in
the bulk and in the boundary versions of the problem. In particular, we find
that the set of points where an FK cluster touches the hull of its surrounding
spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains
this set to points where the neighbouring spin cluster extends to infinity, we
show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are
supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table
Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions
We present an algorithm for enumerating exactly the number of Hamiltonian
chains on regular lattices in low dimensions. By definition, these are sets of
k disjoint paths whose union visits each lattice vertex exactly once. The
well-known Hamiltonian circuits and walks appear as the special cases k=0 and
k=1 respectively. In two dimensions, we enumerate chains on L x L square
lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results
for three dimensions are also given. Using our data we extract several
quantities of physical interest
On the universality of compact polymers
Fully packed loop models on the square and the honeycomb lattice constitute
new classes of critical behaviour, distinct from those of the low-temperature
O(n) model. A simple symmetry argument suggests that such compact phases are
only possible when the underlying lattice is bipartite. Motivated by the hope
of identifying further compact universality classes we therefore study the
fully packed loop model on the square-octagon lattice. Surprisingly, this model
is only critical for loop weights n < 1.88, and its scaling limit coincides
with the dense phase of the O(n) model. For n=2 it is exactly equivalent to the
selfdual 9-state Potts model. These analytical predictions are confirmed by
numerical transfer matrix results. Our conclusions extend to a large class of
bipartite decorated lattices.Comment: 13 pages including 4 figure
Continuous melting of compact polymers
The competition between chain entropy and bending rigidity in compact
polymers can be addressed within a lattice model introduced by P.J. Flory in
1956. It exhibits a transition between an entropy dominated disordered phase
and an energetically favored crystalline phase. The nature of this
order-disorder transition has been debated ever since the introduction of the
model. Here we present exact results for the Flory model in two dimensions
relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We
predict a continuous melting transition, and compute exact values of critical
exponents at the transition point.Comment: 5 pages, 1 figur
Conformational Entropy of Compact Polymers
Exact results for the scaling properties of compact polymers on the square
lattice are obtained from an effective field theory. The entropic exponent
\gamma=117/112 is calculated, and a line of fixed points associated with
interacting chains is identified; along this line \gamma varies continuously.
Theoretical results are checked against detailed numerical transfer matrix
calculations, which also yield a precise estimate for the connective constant
\kappa=1.47280(1).Comment: 4 pages, 1 figur
A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings
Combining tree decomposition and transfer matrix techniques provides a very
general algorithm for computing exact partition functions of statistical models
defined on arbitrary graphs. The algorithm is particularly efficient in the
case of planar graphs. We illustrate it by computing the Potts model partition
functions and chromatic polynomials (the number of proper vertex colourings
using Q colours) for large samples of random planar graphs with up to N=100
vertices. In the latter case, our algorithm yields a sub-exponential average
running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the
exponential running time ~ exp(0.245 N) provided by the hitherto best known
algorithm. We study the statistics of chromatic roots of random planar graphs
in some detail, comparing the findings with results for finite pieces of a
regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded.
Version 3 shows that the worst-case running time is sub-exponential in the
number of vertice
Critical behavior of loops and biconnected clusters on fractals of dimension d < 2
We solve the O(n) model, defined in terms of self- and mutually avoiding
loops coexisting with voids, on a 3-simplex fractal lattice, using an exact
real space renormalization group technique. As the density of voids is
decreased, the model shows a critical point, and for even lower densities of
voids, there is a dense phase showing power-law correlations, with critical
exponents that depend on n, but are independent of density. At n=-2 on the
dilute branch, a trivalent vertex defect acts as a marginal perturbation. We
define a model of biconnected clusters which allows for a finite density of
such vertices. As n is varied, we get a line of critical points of this
generalized model, emanating from the point of marginality in the original loop
model. We also study another perturbation of adding local bending rigidity to
the loop model, and find that it does not affect the universality class.Comment: 14 pages,10 figure
Interacting classical dimers on the square lattice
We study a model of close-packed dimers on the square lattice with a nearest
neighbor interaction between parallel dimers. This model corresponds to the
classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys.
Rev. Lett.{\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix
calculations, we show that this system undergoes a Kosterlitz-Thouless
transition separating a low temperature ordered phase where dimers are aligned
in columns from a high temperature critical phase with continuously varying
exponents. This is understood by constructing the corresponding Coulomb gas,
whose coupling constant is computed numerically. We also discuss doped models
and implications on the finite-temperature phase diagram of quantum dimer
models.Comment: 4 pages, 4 figures; v2 : Added results on doped models; published
versio
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