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

Magnetization Plateaux in Bethe Ansatz Solvable Spin-S Ladders

We examine the properties of the Bethe Ansatz solvable two- and three-leg spin-$S$ ladders. These models include Heisenberg rung interactions of arbitrary strength and thus capture the physics of the spin-$S$ Heisenberg ladders for strong rung coupling. The discrete values derived for the magnetization plateaux are seen to fit with the general prediction based on the Lieb-Schultz- Mattis theorem. We examine the magnetic phase diagram of the spin-1 ladder in detail and find an extended magnetization plateau at the fractional value $= {1/2}$ in agreement with the experimental observation for the spin-1 ladder compound BIP-TENO.Comment: 11 pages, 1 figur

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

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

Exact Solution of an Octagonal Random Tiling Model

We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.Comment: 4 pages,3 Postscript figures, uses revte

On two-point boundary correlations in the six-vertex model with DWBC

The six-vertex model with domain wall boundary conditions (DWBC) on an N x N square lattice is considered. The two-point correlation function describing the probability of having two vertices in a given state at opposite (top and bottom) boundaries of the lattice is calculated. It is shown that this two-point boundary correlator is expressible in a very simple way in terms of the one-point boundary correlators of the model on N x N and (N-1) x (N-1) lattices. In alternating sign matrix (ASM) language this result implies that the doubly refined x-enumerations of ASMs are just appropriate combinations of the singly refined ones.Comment: v2: a reference added, typos correcte

Exact expressions for correlations in the ground state of the dense O(1) loop model

Conjectures for analytical expressions for correlations in the dense O$(1)$ loop model on semi infinite square lattices are given. We have obtained these results for four types of boundary conditions. Periodic and reflecting boundary conditions have been considered before. We give many new conjectures for these two cases and review some of the existing results. We also consider boundaries on which loops can end. We call such boundaries ''open''. We have obtained expressions for correlations when both boundaries are open, and one is open and the other one is reflecting. Also, we formulate a conjecture relating the ground state of the model with open boundaries to Fully Packed Loop models on a finite square grid. We also review earlier obtained results about this relation for the three other types of boundary conditions. Finally, we construct a mapping between the ground state of the dense O$(1)$ loop model and the XXZ spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA

Partition function of the trigonometric SOS model with reflecting end

We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.Comment: 13 pages, improved versio

Non-dispensing pharmacists integrated into general practices as a new interprofessional model:A qualitative evaluation of general practitioners’ experiences and views

Background: A new interprofessional model incorporating non-dispensing pharmacists in general practice teams can improve the quality of pharmaceutical care. However, results of the model are dependent on the context. Understanding when, why and how the model works may increase chances of successful broader implementation in other general practices. Earlier theories suggested that the results of the model are achieved by bringing pharmacotherapeutic knowledge into general practices. This mechanism may not be enough for successful implementation of the model. We wanted to understand better how establishing new interprofessional models in existing healthcare organisations takes place. Methods: An interview study, with a realist informed evaluation was conducted. This qualitative study was part of the Pharmacotherapy Optimisation through Integration of a Non-dispensing pharmacist in primary care Teams (POINT) project. We invited the general practitioners of the 9 general practices who (had) worked closely with a non-dispensing pharmacist for an interview. Interview data were analysed through discussions about the coding with the research team where themes were developed over time. Results: We interviewed 2 general practitioners in each general practice (18 interviews in total). In a context where general practitioners acknowledge the need for improvement and are willing to work with a non-dispensing pharmacist as a new team member, the following mechanisms are triggered. Non-dispensing pharmacists add new knowledge to current general practice. Through everyday talk (discursive actions) both general practitioners and non-dispensing pharmacists evolve in what they consider appropriate, legitimate and imaginable in their work situations. They align their professional identities. Conclusions: Not only the addition of new knowledge of non-dispensing pharmacist to the general practice team is crucial for the success of this interprofessional healthcare model, but also alignment of the general practitioners’ and non-dispensing pharmacists’ professional identities. This is essentially different from traditional pharmaceutical care models, in which pharmacists and GPs work in separate organisations. To induce the process of identity alignment, general practitioners need to acknowledge the need to improve the quality of pharmaceutical care interprofessionally. By acknowledging the aspect of interprofessionality, both general practitioners and non-dispensing pharmacists will explore and reflect on what they consider appropriate, legitimate and imaginable in carrying out their professional roles. Trial registration: The POINT project was pre-registered in The Netherlands National Trial Register, with Trial registration number NTR-4389.</p

The scleractinian <i>Agaricia undata</i> as a new host for the coral-gall crab <i>Opecarcinus hypostegus</i> at Bonaire, southern Caribbean

The Caribbean scleractinian reef coral Agaricia undata (Agariciidae) is recorded for the first time as a host of the coral-gall crab Opecarcinus hypostegus (Cryptochiridae). The identity of the crab was confirmed with the help of DNA barcoding. The association has been documented with photographs taken in situ at 25 m depth and in the laboratory. The predominantly mesophotic depth range of the host species suggests this association to be present also at greater depths. With this record, all seven Agaricia species are now listed as gall-crab hosts, together with the agariciid Helioseris cucullata. Within the phylogeny of Agariciidae, Helioseris is not closely related to Agaricia. Therefore, the association between Caribbean agariciids and their gall-crab symbionts may either have originated early in their shared evolutionary history or later as a result of host range expansion. New information on coral-associated fauna, such as what is presented here, leads to a better insight on the diversity, evolution, and ecology of coral reef biota, particularly in the Caribbean, where cryptochirids have rarely been studied.</p