1,437 research outputs found
Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
The raise and peel model of a one-dimensional fluctuating interface (model A)
is extended by considering one source (model B) or two sources (model C) at the
boundaries. The Hamiltonians describing the three processes have, in the
thermodynamic limit, spectra given by conformal field theory. The probability
of the different configurations in the stationary states of the three models
are not only related but have interesting combinatorial properties. We show
that by extending Pascal's triangle (which gives solutions to linear relations
in terms of integer numbers), to an hexagon, one obtains integer solutions of
bilinear relations. These solutions give not only the weights of the various
configurations in the three models but also give an insight to the connections
between the probability distributions in the stationary states of the three
models. Interestingly enough, Pascal's hexagon also gives solutions to a
Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few
references are adde
A refined Razumov-Stroganov conjecture II
We extend a previous conjecture [cond-mat/0407477] relating the
Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to
refined numbers of alternating sign matrices. By considering the O(1) loop
model on a semi-infinite cylinder with dislocations, we obtain the generating
function for alternating sign matrices with prescribed positions of 1's on
their top and bottom rows. This seems to indicate a deep correspondence between
observables in both models.Comment: 21 pages, 10 figures (3 in text), uses lanlmac, hyperbasics and epsf
macro
Supersymmetry on Jacobstahl lattices
It is shown that the construction of Yang and Fendley (2004 {\it J. Phys. A:
Math.Gen. {\bf 37}} 8937) to obtainsupersymmetric systems, leads not to the
open XXZ chain with anisotropy but to systems having
dimensions given by Jacobstahl sequences.For each system the ground state is
unique. The continuum limit of the spectra of the Jacobstahl systems coincide,
up to degeneracies, with that of the invariant XXZ chain for
. The relation between the Jacobstahl systems and the open XXZ
chain is explained.Comment: 6 pages, 0 figure
Chronic GLP-1 receptor activation by exendin-4 induces expansion of pancreatic duct glands in rats and accelerates formation of dysplastic lesions and chronic pancreatitis in the Kras(G12D) mouse model.
Pancreatic duct glands (PDGs) have been hypothesized to give rise to pancreatic intraepithelial neoplasia (PanIN). Treatment with the glucagon-like peptide (GLP)-1 analog, exendin-4, for 12 weeks induced the expansion of PDGs with mucinous metaplasia and columnar cell atypia resembling low-grade PanIN in rats. In the pancreata of Pdx1-Cre; LSL-Kras(G12D) mice, exendin-4 led to acceleration of the disruption of exocrine architecture and chronic pancreatitis with mucinous metaplasia and increased formation of murine PanIN lesions. PDGs and PanIN lesions in rodent and human pancreata express the GLP-1 receptor. Exendin-4 induced proproliferative signaling pathways in human pancreatic duct cells, cAMP-protein kinase A and mitogen-activated protein kinase phosphorylation of cAMP-responsive element-binding protein, and increased cyclin D1 expression. These GLP-1 effects were more pronounced in the presence of an activating mutation of Kras and were inhibited by metformin. These data reveal that GLP-1 mimetic therapy may induce focal proliferation in the exocrine pancreas and, in the context of exocrine dysplasia, may accelerate formation of neoplastic PanIN lesions and exacerbate chronic pancreatitis
The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance
The raise and peel model describes the stochastic model of a fluctuating
interface separating a substrate covered with clusters of matter of different
sizes, and a rarefied gas of tiles. The stationary state is obtained when
adsorption compensates the desorption of tiles. This model is generalized to an
interface with defects (D). The defects are either adjacent or separated by a
cluster. If a tile hits the end of a cluster with a defect nearby, the defect
hops at the other end of the cluster changing its shape. If a tile hits two
adjacent defects, the defect annihilate and are replaced by a small cluster.
There are no defects in the stationary state.
This model can be seen as describing the reaction D + D -->0, in which the
particles (defects) D hop at long distances changing the medium and annihilate.
Between the hops the medium also changes (tiles hit clusters changing their
shapes). Several properties of this model are presented and some exact results
are obtained using the connection of our model with a conformal invariant
quantum chain.Comment: 8 pages, 12figure
Finite-size left-passage probability in percolation
We obtain an exact finite-size expression for the probability that a
percolation hull will touch the boundary, on a strip of finite width. Our
calculation is based on the q-deformed Knizhnik--Zamolodchikov approach, and
the results are expressed in terms of symplectic characters. In the large size
limit, we recover the scaling behaviour predicted by Schramm's left-passage
formula. We also derive a general relation between the left-passage probability
in the Fortuin--Kasteleyn cluster model and the magnetisation profile in the
open XXZ chain with diagonal, complex boundary terms.Comment: 21 pages, 8 figure
Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
The asymmetric simple exclusion process with open boundaries, which is a very
simple model of out-of-equilibrium statistical physics, is known to be
integrable. In particular, its spectrum can be described in terms of Bethe
roots. The large deviation function of the current can be obtained as well by
diagonalizing a modified transition matrix, that is still integrable: the
spectrum of this new matrix can be also described in terms of Bethe roots for
special values of the parameters. However, due to the algebraic framework used
to write the Bethe equations in the previous works, the nature of the
excitations and the full structure of the eigenvectors were still unknown. This
paper explains why the eigenvectors of the modified transition matrix are
physically relevant, gives an explicit expression for the eigenvectors and
applies it to the study of atypical currents. It also shows how the coordinate
Bethe Ansatz developped for the excitations leads to a simple derivation of the
Bethe equations and of the validity conditions of this Ansatz. All the results
obtained by de Gier and Essler are recovered and the approach gives a physical
interpretation of the exceptional points The overlap of this approach with
other tools such as the matrix Ansatz is also discussed. The method that is
presented here may be not specific to the asymmetric exclusion process and may
be applied to other models with open boundaries to find similar exceptional
points.Comment: references added, one new subsection and corrected typo
Refined Razumov-Stroganov conjectures for open boundaries
Recently it has been conjectured that the ground-state of a Markovian
Hamiltonian, with one boundary operator, acting in a link pattern space is
related to vertically and horizontally symmetric alternating-sign matrices
(equivalently fully-packed loop configurations (FPL) on a grid with special
boundaries).We extend this conjecture by introducing an arbitrary boundary
parameter. We show that the parameter dependent ground state is related to
refined vertically symmetric alternating-sign matrices i.e. with prescribed
configurations (respectively, prescribed FPL configurations) in the next to
central row.
We also conjecture a relation between the ground-state of a Markovian
Hamiltonian with two boundary operators and arbitrary coefficients and some
doubly refined (dependence on two parameters) FPL configurations. Our
conjectures might be useful in the study of ground-states of the O(1) and XXZ
models, as well as the stationary states of Raise and Peel models.Comment: 11 pages LaTeX, 8 postscript figure
Conformal invariance and its breaking in a stochastic model of a fluctuating interface
Using Monte-Carlo simulations on large lattices, we study the effects of
changing the parameter (the ratio of the adsorption and desorption rates)
of the raise and peel model. This is a nonlocal stochastic model of a
fluctuating interface. We show that for the system is massive, for
it is massless and conformal invariant. For the conformal
invariance is broken. The system is in a scale invariant but not conformal
invariant phase. As far as we know it is the first example of a system which
shows such a behavior. Moreover in the broken phase, the critical exponents
vary continuously with the parameter . This stays true also for the critical
exponent which characterizes the probability distribution function of
avalanches (the critical exponent staying unchanged).Comment: 22 pages and 20 figure
Six - Vertex Model with Domain wall boundary conditions. Variable inhomogeneities
We consider the six-vertex model with domain wall boundary conditions. We
choose the inhomogeneities as solutions of the Bethe Ansatz equations. The
Bethe Ansatz equations have many solutions, so we can consider a wide variety
of inhomogeneities. For certain choices of the inhomogeneities we study arrow
correlation functions on the horizontal line going through the centre. In
particular we obtain a multiple integral representation for the emptiness
formation probability that generalizes the known formul\ae for XXZ
antiferromagnets.Comment: 12 pages, 1 figur
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