Free energy of the random Ising model in terms of the magnetizations of sites

1983 ◽  
Vol 119 (1-2) ◽  
pp. 143-152 ◽  
Author(s):  
T. Morita
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Random Ising Model

Free-energy fluctuations in a one-dimensional random Ising model

1989 ◽  
Vol 39 (6) ◽  
pp. 3170-3172 ◽  
Author(s):  
Toshijiro Tanaka ◽  
Hirokazu Fujisaka ◽  
Masayoshi Inoue
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
One Dimensional ◽  
Random Ising Model

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

Extended high temperature low field expansions for the Ising model

1979 ◽  
Vol 57 (8) ◽  
pp. 1239-1245 ◽  
Author(s):  
S. McKenzie
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Ising Model ◽  
Three Dimensional ◽  
Low Field ◽  
Hypercubic Lattice

High temperature low field expansions are derived from the free energy of the Ising model for several two- and three-dimensional lattices. These represent a considerable advance on earlier work. Expansions for the four-dimensional hypercubic lattice are also presented.

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