Corner transfer matrices in statistical mechanics

Corner transfer matrices are a useful tool in the statistical mechanics of simple two-dimensinal models. They can be very effective way of obtaining series expansions of unsolved models, and of calculating the order parameters of solved ones. Here we review these features and discuss the reason why the method fails to give the order parameter of the chiral Potts model.Comment: 18 pages, 4 figures, for Proceedings of Conference on Symmetries and Integrability of Difference Equations. (SIDE VII), Melbourne, July 200

The order parameter of the chiral Potts model

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but as far as the author is aware there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ``broken rapidity line'' approach pioneered by Jimbo, Miwa and Nakayashiki.Comment: 29 pages, 7 figures. Citations made more explicit and some typos correcte

New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity

The Q matrix invented by Baxter in 1972 to solve the eight vertex model at roots of unity exists for all values of N, the number of sites in the chain, but only for a subset of roots of unity. We show in this paper that a new Q matrix, which has recently been introduced and is non zero only for N even, exists for all roots of unity. In addition we consider the relations between all of the known Q matrices of the eight vertex model and conjecture functional equations for them.Comment: 20 pages, 2 Postscript figure

Integrability of qq-oscillator lattice model

A simple formulation of an exactly integrable $q$-oscillator model on two dimensional lattice (in 2+1 dimensional space-time) is given. Its interpretation in the terms of 2d quantum inverse scattering method and nested Bethe Ansatz equations is discussed.Comment: Talk given at the conference ``New frontiers in exactly solved models'', ANU, July 21-22, 200

Benefits and losses: a qualitative study exploring healthcare staff perceptions of teamworking

ABSTRACT Objectives: To examine staff perceptions of teamworking practice in the field of stroke care. Design: Qualitative interview study. Setting: Three teams providing care to patients with stroke across a typical care pathway of acute hospital ward, specialist stroke unit, and community rehabilitation. Participants: 37 staff members from a range of professions. Main outcome measures: Healthcare staff perceptions of teamworking. Results: Through detailed coding and analysis of the transcripts, five perceptions regarding the impact of teamworking on staff and patients were identified. These were: (1) mutual staff support, (2) knowledge and skills sharing, (3) timely intervention/discharge, (4) reduced individual decision-making and responsibility and (5) impact on patient contact time. Conclusions: Teamworking practice may be associated with a number of perceived benefits for staff and patient care; however, the potential for losses resulting from reduced patient contact time and ill-defined responsibility needs further investigation

Two-dimensional Rydberg gases and the quantum hard squares model

We study a two-dimensional lattice gas of atoms that are photo-excited to high-lying Rydberg states in which they interact via the van-der-Waals interaction. We explore the regime of dominant nearest neighbor interaction where this system is intimately connected to a quantum version of Baxter's hard squares model. We show that the strongly correlated ground state of the Rydberg gas can be analytically described by a projected entangled pair state that constitutes the ground state of the quantum hard squares model. This correspondence allows us to identify a first order phase boundary where the Rydberg gas undergoes a transition from a disordered (liquid) phase to an ordered (solid) phase

Analyticity and Integrabiity in the Chiral Potts Model

We study the perturbation theory for the general non-integrable chiral Potts model depending on two chiral angles and a strength parameter and show how the analyticity of the ground state energy and correlation functions dramatically increases when the angles and the strength parameter satisfy the integrability condition. We further specialize to the superintegrable case and verify that a sum rule is obeyed.Comment: 31 pages in harvmac including 9 tables, several misprints eliminate

Yang-Baxter R operators and parameter permutations

We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the tensor product of two representations of the symmetry algebra with arbitrary spins $\ell_1$ and $\ell_2$ is built in terms of products of three basic operators $\mathcal{S}_1, \mathcal{S}_2,\mathcal{S}_3$ which are constructed explicitly. They have the simple meaning of representing elementary permutations of the symmetric group $\mathfrak{S}_4$, the permutation group of the four parameters entering the RLL-relation.Comment: 22 pages LaTex, comments added, version to be published in Nucl. Phys.