Boundary operators in the O(n) and RSOS matrix models

We study the new boundary condition of the O(n) model proposed by Jacobsen and Saleur using the matrix model. The spectrum of boundary operators and their conformal weights are obtained by solving the loop equations. Using the diagrammatic expansion of the matrix model as well as the loop equations, we make an explicit correspondence between the new boundary condition of the O(n) model and the "alternating height" boundary conditions in RSOS model.Comment: 29 pages, 4 figures; version to appear in JHE

La ocupación como sustituto de la estimación de la abundancia

In many monitoring programmes it may be prohibitively expensive to estimate the actual abundance of a bird species in a defined area, particularly at large spatial scales, or where birds occur at very low densities. Often it may be appropriate to consider the proportion of area occupied by the species as an alternative state variable. However, as with abundance estimation, issues of detectability must be taken into account in order to make accurate inferences: the non–detection of the species does not imply the species is genuinely absent. Here we review some recent modelling developments that permit unbiased estimation of the proportion of area occupied, colonization and local extinction probabilities. These methods allow for unequal sampling effort and enable covariate information on sampling locations to be incorporated. We also describe how these models could be extended to incorporate information from marked individuals, which would enable finer questions of population dynamics (such as turnover rate of nest sites by specific breeding pairs) to be addressed. We believe these models may be applicable to a wide range of bird species and may be useful for investigating various questions of ecological interest. For example, with respect to habitat quality, we might predict that a species is more likely to have higher local extinction probabilities, or higher turnover rates of specific breeding pairs, in poor quality habitats.En muchos programas de monitorización puede resultar extremadamente caro estimar la abundancia real de una especie de ave en un área definida, especialmente a grandes escalas espaciales, o donde las aves se dan a densidades muy bajas. A menudo, es posible que resulte conveniente considerar la proporción del área ocupada por la especie como una variable de estado alternativa. Sin embargo, al igual que sucede con la estimación de la abundancia, para poder realizar deducciones exactas es preciso tener en cuenta ciertas cuestiones de detectabilidad: el hecho de que una especie no pueda detectarse no significa que realmente esté ausente. En este estudio analizamos algunos modelos de reciente desarrollo que permiten una estimación no sesgada de la proporción del área ocupada, de la colonización y de las probabilidades de extinción local. Estos métodos permiten un esfuerzo de muestreo desigual, así como la posibilidad de incorporar información sobre covariantes en los emplazamientos de muestreo. También describimos el procedimiento para ampliarlos a fin de incorporar información acerca de individuos marcados, lo que permitiría abordar con mayor detalle cuestiones acerca de la dinámica poblacional (como el índice de rotación de los emplazamientos de los nidos por parte de parejas de reproducción específicas). Consideramos que estos modelos podrían aplicarse a una amplia gama de especies de aves, pudiendo resultar útiles para investigar diversas cuestiones de interés ecológico. Por ejemplo, respecto a la calidad del hábitat, podríamos predecir que una especie presenta más probabilidades de extinción local, o índices de rotación más elevados de determinadas parejas de reproducción, en hábitats de baja calidad

Structure of the two-boundary XXZ model with non-diagonal boundary terms

We study the integrable XXZ model with general non-diagonal boundary terms at both ends. The Hamiltonian is considered in terms of a two boundary extension of the Temperley-Lieb algebra. We use a basis that diagonalizes a conserved charge in the one-boundary case. The action of the second boundary generator on this space is computed. For the L-site chain and generic values of the parameters we have an irreducible space of dimension 2^L. However at certain critical points there exists a smaller irreducible subspace that is invariant under the action of all the bulk and boundary generators. These are precisely the points at which Bethe Ansatz equations have been formulated. We compute the dimension of the invariant subspace at each critical point and show that it agrees with the splitting of eigenvalues, found numerically, between the two Bethe Ansatz equations.Comment: 9 pages Latex. Minor correction

Boundary changing operators in the O(n) matrix model

We continue the study of boundary operators in the dense O(n) model on the random lattice. The conformal dimension of boundary operators inserted between two JS boundaries of different weight is derived from the matrix model description. Our results are in agreement with the regular lattice findings. A connection is made between the loop equations in the continuum limit and the shift relations of boundary Liouville 3-points functions obtained from Boundary Ground Ring approach.Comment: 31 pages, 4 figures, Introduction and Conclusion improve

Equivalences between spin models induced by defects

The spectrum of integrable spin chains are shown to be independent of the ordering of their spins. As an application we introduce defects (local spin inhomogeneities in homogenous chains) in two-boundary spin systems and, by changing their locations, we show the spectral equivalence of different boundary conditions. In particular we relate certain nondiagonal boundary conditions to diagonal ones.Comment: 14 pages, 16 figures, LaTeX, Extended versio

Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity

We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are arbitrary, and need not satisfy any constraint. The solution is in terms of generalized T - Q equations, having more than one Q function. We find numerical evidence that this solution gives the complete set of 2^N transfer matrix eigenvalues, where N is the number of spins.Comment: 22 page