Eight-vertex model and Ising model in a non-zero magnetic field: honeycomb lattice

1990 ◽  
Vol 23 (3) ◽  
pp. 375-378 ◽  
Author(s):  
F Y Wu
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Zero Magnetic Field ◽  
Honeycomb Lattice ◽  
Vertex Model

GENERAL 8-VERTEX MODEL ON THE HONEYCOMB LATTICE: EQUIVALENCE WITH AN ISING MODEL

1990 ◽  
Vol 04 (05) ◽  
pp. 311-316 ◽  
Author(s):  
K. Y. LIN ◽  
F. Y. WU
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Honeycomb Lattice ◽  
Vertex Model ◽  
Independent Vertex ◽  
Anisotropic Interactions ◽  
Complex Magnetic Field

It is shown that the general 8-vertex model on the honeycomb lattice is always reducible to an Ising model in a nonzero but generally complex magnetic field. In the most general case of the staggered 8-vertex model characterized by 16 independent vertex weights, the equivalent Ising model has three anisotropic interactions and a staggered magnetic field which assumes two different values on the two sublattices.

Exact Results for a Model Ternary Polymer Mixture

1997 ◽  
Vol 11 (01n02) ◽  
pp. 169-174
Author(s):  
P. Pant ◽  
F. Y. Wu ◽  
J. H. Barry
Keyword(s):  
Magnetic Field ◽  
Zero Magnetic Field ◽  
Polymer Mixture ◽  
Honeycomb Lattice ◽  
Exact Results ◽  
Vertex Model ◽  
Two Phase ◽  
Functional Monomers ◽  
Composition Space ◽  
Ternary Polymer

A model ternary polymer mixture is considered with bi- and -functional monomers and a solvent embedded on a honeycomb lattice. The model is shown to be equivalent to an eight-vertex model on the same lattice. Using this equivalence which further maps the problem into an Ising model in a non-zero magnetic field, an exact analysis of the model is carried out. The two phase coexistence surface in the temperature- composition space is determined exactly and connectivity properties of the model are studied.

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