scholarly journals Ising Model on a Triangular Lattice with Three-spin Interactions. I. Free Energy and Correlation Length

1974 ◽  
Vol 27 (3) ◽  
pp. 369 ◽  
Author(s):  
RJ Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Bethe Ansatz ◽  
Correlation Length ◽  
Triangular Lattice ◽  
Hexagonal Lattice ◽  
Spin Interactions

Following the demonstration in Part I that the Ising mogel with three-spin interactions on a triangular lattice is equivalent to a colouring problem on a hexagonal lattice, and that a generalized Bethe ansatz can be used to obtain equations for the eigenv

scholarly journals Ising Model on a Triangular Lattice with Three-spin Interactions. I. The Eigenvalue Equation

1974 ◽  
Vol 27 (3) ◽  
pp. 357 ◽  
Author(s):  
RJ Baxter ◽  
FY Wu
Keyword(s):  
Ising Model ◽  
Transfer Matrix ◽  
Triangular Lattice ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Hexagonal Lattice ◽  
Eigenvalue Equation ◽  
Spin Interactions ◽  
A Site

It is shown that the Ising model with three-spin interactions on a triangular lattice is equivalent to a site-colouring problem on a hexagonal lattice. The transfer matrix method is then used to solve the colouring problem. The colouring of two neighbouri

Analytic properties of the Ising model with triplet interactions on the triangular lattice

1975 ◽  
Vol 343 (1632) ◽  
pp. 45-62 ◽  
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Explicit Form ◽  
Triangular Lattice

The analytic properties of the Baxter-W u solution for the Ising model with pure triplet interactions on the triangular lattice are investigated. In particular, it is shown that the free energy per spin of the model can be written in the explicit form

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

The stationarity of the free energy in the Ising model of spin glasses

1981 ◽  
Vol 85 (5) ◽  
pp. 301-302
Author(s):  
V.A. Moskalenko ◽  
L.A. Dogotar ◽  
M.I. Vladimir
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Spin Glasses
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