The three-spin Ising model as an eight-vertex model

1976 ◽  
Vol 9 (10) ◽  
pp. L149-L152 ◽  
Author(s):  
R J Baxter ◽  
I G Enting
Keyword(s):  
Ising Model ◽  
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.

scholarly journals Correlation Functions of the Ising Model with Multisite Interaction on the Husimi Lattice

1998 ◽  
Vol 12 (23) ◽  
pp. 2349-2358 ◽  
Author(s):  
N. S. Ananikian ◽  
R. G. Ghulghazaryan ◽  
N. Sh. Izmailian
Keyword(s):  
Ising Model ◽  
Fixed Points ◽  
Coordination Number ◽  
Recurrence Relation ◽  
Correlation Functions ◽  
Nearest Neighbor ◽  
Bethe Lattice ◽  
Vertex Model ◽  
Analytical Expression ◽  
Husimi Lattice

We consider a general spin-1/2 Ising model with multisite interaction on the Husimi lattice with the coordination number q and derive an analytical expression of correlation functions for stable fixed points of the corresponding recurrence relation. We show that for q=2 our model transforms to the two-state vertex model on the Bethe lattice with q=3 and for the case q=3, with only nearest neighbor interactions, we transform our model to the corresponding model on the Bethe lattice with q=3, using the Yang–Baxter equations.

GAUGE TRANSFORMATION AND VERTEX MODELS: A POLYNOMIAL FORMULATION

1995 ◽  
Vol 09 (24) ◽  
pp. 3209-3217 ◽  
Author(s):  
G. ROLLET ◽  
F. Y. WU
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Gauge Transformation ◽  
Vertex Model ◽  
Arbitrary Graph ◽  
Vertex Models ◽  
Polynomial Formulation

We consider vertex models on an arbitrary graph and propose a new polynomial formulation for its gauge transformation under which the partition function is invariant. Our formulation recovers in a simple way various, previously obtained results including the condition under which the vertex model is equivalent to an Ising model.

Sign in / Sign up

Export Citation Format

Share Document