Deriving exact results for Ising-like models from the cluster variation method

The cluster variation method (CVM) is an approximation technique which generalizes the mean field approximation and has been widely applied in the last decades, mainly for finding accurate phase diagrams of Ising-like lattice models. Here we discuss in which cases the CVM can yield exact results, considering: (i) one-dimensional systems and strips (in which case the method reduces to the transfer matrix method), (ii) tree-like lattices and (iii) the so-called disorder points of euclidean lattice models with competitive interactions in more than one dimension.Comment: 3 pages, presented at Lattice '9

A New Solution of the Yang-Baxter Equation Related to the Adjoint Representation of UqB2U_{q}B_{2}

A new solution of the Yang-Baxter equation, that is related to the adjoint representation of the quantum enveloping algebra $U_{q}B_{2}$, is obtained by fusion formulas from a non-standard solution.Comment: 16 pages (Latex), Preprint BIHEP-TH-93-3

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of $n$. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O($n$) branch for $n < 2$ and the results obtained by previous transfer matrix calculations. For $n=2$, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model. These results confirm that the cubic anisotropy is marginal at $n=2$ but irrelevant for $n<2$

Radiographic viewing conditions at Johannesburg Hospital

Purpose: To measure the luminance level of X-ray viewing boxes and ambient lighting levels in reporting rooms as a quality assurance procedure, and to compare the results with those recommended by the Directorate of Radiatio

Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros

We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a similar discussion for the Potts model with $q=3$ on the honeycomb lattice and with $q=3,4$ on the kagom\'e lattice.Comment: 33 pages, Latex, 9 encapsulated postscript figures, J. Phys. A, in pres

An operator approach to the rational solutions of the classical Yang-Baxter equation

Motivated by the study of the operator forms of the constant classical Yang-Baxter equation given by Semonov-Tian-Shansky, Kupershmidt and the others, we try to construct the rational solutions of the classical Yang-Baxter equation with parameters by certain linear operators. The fact that the rational solutions of the CYBE for the simple complex Lie algebras can be interpreted in term of certain linear operators motivates us to give the notion of $\mathcal O$-operators such that these linear operators are the $\mathcal O$-operators associated to the adjoint representations. Such a study can be generalized to the Lie algebras with nondegenerate symmetric invariant bilinear forms. Furthermore we give a construction of a rational solution of the CYBE from an $\mathcal O$-operator associated to the coadjoint representation and an arbitrary representation with a trivial product in the representation space respectively.Comment: 23page

Cluster variation method and disorder varieties of two-dimensional Ising-like models

I show that the cluster variation method, long used as a powerful hierarchy of approximations for discrete (Ising-like) two-dimensional lattice models, yields exact results on the disorder varieties which appear when competitive interactions are put into these models. I consider, as an example, the plaquette approximation of the cluster variation method for the square lattice Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions, and, after rederiving known results, report simple closed-form expressions for the pair and plaquette correlation functions.Comment: 10 revtex pages, 1 postscript figur

An investigation into the depth of penetration of low level laser therapy through the equine tendon in vivo

Low level laser therapy (LLLT) is frequently used in the treatment of wounds, soft tissue injury and in pain management. The exact penetration depth of LLLT in human tissue remains unspecified. Similar uncertainty regarding penetration depth arises in treating animals. This study was designed to test the hypothesis that transmission of LLLT in horses is increased by clipping the hair and/or by cleaning the area to be treated with alcohol, but is unaffected by coat colour. A LLLT probe (810 nm, 500 mW) was applied to the medial aspect of the superficial flexor tendon of seventeen equine forelimbs in vivo. A light sensor was applied to the lateral aspect, directly opposite the laser probe to measure the amount of light transmitted. Light transmission was not affected by individual horse, coat colour or leg. However, it was associated with leg condition (F = 4.42, p = 0.0032). Tendons clipped dry and clipped and cleaned with alcohol, were both associated with greater transmission of light than the unprepared state. Use of alcohol without clipping was not associated with an increase in light transmission. These results suggest that, when applying laser to a subcutaneous structure in the horse, the area should be clipped and cleaned beforehand

Quivers, YBE and 3-manifolds

We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a "Z-invariant" lattice on T^2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in H^3, each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph.The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results.Comment: 61 pages, 16 figures; v2: typos correcte

Folding transitions of the triangular lattice with defects

A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest-neighbor and plaquette interactions on the honeycomb lattice. Its phase diagram is determined in the hexagon approximation of the cluster variation method and the crossover from the pure Ising to the pure folding model is investigated, obtaining a quite rich structure with several multicritical points. Our results are in very good agreement with the available exact ones and extend a previous transfer matrix study.Comment: 16 pages, latex, 5 postscript figure