A duality theorem for planar three-body Ising models and their vertex model equivalences

1977 ◽  
Vol 10 (2) ◽  
pp. 229-238 ◽  
Author(s):  
D W Wood ◽  
N E Pegg
Keyword(s):  
Duality Theorem ◽  
Ising Models ◽  
Vertex Model ◽  
Three Body

Solvable eight-vertex model on an arbitrary planar lattice

1978 ◽  
Vol 289 (1359) ◽  
pp. 315-346 ◽  
Keyword(s):  
Statistical Mechanics ◽  
Solvable Model ◽  
Ising Models ◽  
Square Lattice ◽  
Vertex Model ◽  
Temperature Dependent ◽  
Planar Lattice ◽  
Special Cases ◽  
Local Properties ◽  
Straight Lines

Any planar set of intersecting straight lines forms a four-coordinated graph, or ‘lattice’, provided no three lines intersect at a point. For any such lattice an eight-vertex model can be constructed. Provided the interactions satisfy certain constraints (which are in general temperature-dependent), the model can be solved exactly in the thermodynamic limit, its local properties at a particular site being those of a related square lattice. A particular case is a solvable model on the Kagomé lattice. It is shown that this model includes as special cases many of the models in statistical mechanics that have been solved exactly, notably the square, triangular and honeycomb Ising models, and the square eight-vertex model. Some remarkable equivalences between correlations on different lattices are also established.

MAPPING OF p-STATE SYMMETRIC VERTEX MODEL ON THE HONEYCOMB LATTICE ONTO ITS ISING-SPIN COUNTERPART

1992 ◽  
Vol 06 (02) ◽  
pp. 251-260 ◽  
Author(s):  
L. ŠAMAJ ◽  
M. KOLESÍK
Keyword(s):  
Ising Model ◽  
Parameter Space ◽  
Ising Models ◽  
Honeycomb Lattice ◽  
Model Parameters ◽  
Vertex Model ◽  
Free Energies ◽  
Gauge Transformations ◽  
Ising Spin ◽  
Arbitrary Lattice

The mapping which produces a path between the p-state symmetric vertex model and the Ising model with spin [Formula: see text] on the honeycomb lattice is constructed. The mapping construction is based on a combination of decoration and gauge transformations. The formulation enables one to find the manifold in the vertex weights parameter space on which the mapping can be performed and to derive dual relations among the model parameters as well as the free energies of related symmetric vertex and Ising models. The extension of the mapping to arbitrary lattice coordination is outlined.

scholarly journals Error Threshold for Color Codes and Random Three-Body Ising Models

2009 ◽  
Vol 103 (9) ◽  
Author(s):  
Helmut G. Katzgraber ◽  
H. Bombin ◽  
M. A. Martin-Delgado
Keyword(s):  
Ising Models ◽  
Error Threshold ◽  
Three Body

Erratum - Frustration in periodic systems : exact results for some 2D ising models

1979 ◽  
Vol 40 (10) ◽  
pp. 1024-1024
Author(s):  
G. André ◽  
R. Bidaux ◽  
J.-P. Carton ◽  
R. Conte ◽  
L. de Seze
Keyword(s):  
Ising Models ◽  
Periodic Systems ◽  
Exact Results
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