Multicritical two-dimensional vertex models

1992 ◽  
Vol 46 (2) ◽  
pp. R703-R706 ◽  
Author(s):  
Somendra M. Bhattacharjee ◽  
J. J. Rajasekaran
Keyword(s):  
Two Dimensional ◽  
Vertex Models

FROM INHOMOGENEOUS SIX-VERTEX LATTICE MODELS TO CONTINUUM QUANTUM INTEGRABLE MODELS

1992 ◽  
Vol 07 (25) ◽  
pp. 6385-6403
Author(s):  
Y.K. ZHOU
Keyword(s):  
Integrable Systems ◽  
Scaling Limit ◽  
Lattice Models ◽  
Integrable Models ◽  
Two Dimensional ◽  
Vertex Model ◽  
Quantum Integrable Systems ◽  
Vertex Models ◽  
Quantum Integrable Models ◽  
Sine Gordon Model

A method to find continuum quantum integrable systems from two-dimensional vertex models is presented. We explain the method with the example where the quantum sine-Gordon model is obtained from an inhomogeneous six-vertex model in its scaling limit. We also show that the method can be applied to other models.

CRITICAL SPIN-1 VERTEX MODELS AND O(n) MODELS

1990 ◽  
Vol 04 (05) ◽  
pp. 929-942 ◽  
Author(s):  
Bernard NIENHUIS
Keyword(s):  
Critical Points ◽  
Critical Exponents ◽  
Square Lattice ◽  
Two Dimensional ◽  
Planar Lattice ◽  
Vertex Models ◽  
Critical Manifold ◽  
Multicritical Points ◽  
Straightforward Generalization

A method is presented by which critical and multicritical points of spin-1 (three-state) vertex models and classical O(n) models on two-dimensional lattices are determined. It is a straightforward generalization of the ideas that earlier led to the determination of critical points and critical exponents of a honeycomb O(n) model. On the square lattice the methods leads to tricritical as well as critical loci. For n=2 a larger critical manifold is found than for other values of n. At the critical and multicritical points thus produced the models turn out to be soluble. The method is applicable to O(n) models and spin-1 vertex models on any planar lattice.

scholarly journals ON THE SYMMETRIES OF INTEGRABILITY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 1881-1903 ◽  
Author(s):  
M. BELLON ◽  
J-M. MAILLARD ◽  
C. VIALLET
Keyword(s):  
Quantum Groups ◽  
Discrete Group ◽  
Three Dimensional ◽  
Algebraic Combinatorics ◽  
Two Dimensional ◽  
Algebraic Varieties ◽  
Spin Models ◽  
Projective Transformations ◽  
Vertex Models ◽  
Higher Dimensional

We show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group [Formula: see text]. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. We mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. Our results also yield the generalization of the condition qn=1 so often mentioned in the theory of quantum groups, when no q parameter is available.

Vertex models for two-dimensional grain growth

1989 ◽  
Vol 60 (3) ◽  
pp. 399-421 ◽  
Author(s):  
Kyozi Kawasaki ◽  
Tatsuzo Nagai ◽  
Katsuya Nakashima
Keyword(s):  
Grain Growth ◽  
Two Dimensional ◽  
Vertex Models

NEW LOCAL RELATIONS FOR LATTICE MODELS

1990 ◽  
Vol 04 (11n12) ◽  
pp. 1895-1912 ◽  
Author(s):  
J. AVAN ◽  
J-M. MAILLARD ◽  
M. TALON ◽  
C. VIALLET
Keyword(s):  
Lattice Models ◽  
Two Dimensional ◽  
Transfer Matrices ◽  
Arbitrary Size ◽  
Vertex Models ◽  
Hard Hexagon Model

We describe new local relations leading to non-trivial (non-homogeneous) equations for the row-to-row transfer matrices of arbitrary size for two dimensional I.R.F. and vertex models. We sketch the connection between this relation and the Yang-Baxter equations, and we describe the example of the hard hexagon model.

scholarly journals Interplay of curvature and rigidity in shape-based models of confluent tissue

2020 ◽  
Author(s):  
Daniel M. Sussman
Keyword(s):  
Cell Motility ◽  
Biological Tissue ◽  
Finite Temperature ◽  
Transition Point ◽  
Shape Index ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Temperature Transition ◽  
Vertex Models ◽  
Geodesic Distances

Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity in two-dimensional vertex models confined to the surface of a sphere. By considering shapes of cells defined by perimeters whose magnitude depends on geodesic distances and areas determined by spherical polygons, the critical shape index in such models is affected by the size of the cell relative to the radius of the sphere on which it is embedded. This implies that cells can collectively rigidify by growing the size of the sphere, i.e. by tuning the curvature of their domain. Finite-temperature studies indicate that cell motility is affected well away from the zero-temperature transition point.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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