Entropy and free energy of the spin glass in the random-bond Ising model on the square lattice at finite temperatures

1982 ◽  
Vol 116 (3) ◽  
pp. 622
Author(s):  
Nahomi Miyamoto ◽  
Shigetoshi Katsura
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Spin Glass ◽  
Square Lattice

ISING MODEL ON A LAYERED SQUARE LATTICE

1989 ◽  
Vol 03 (07) ◽  
pp. 1119-1128
Author(s):  
K.Y. LIN ◽  
K.J. HSU
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Ising Model ◽  
Transfer Matrix ◽  
Square Lattice ◽  
The Magnetic Field

We have considered the Ising model on a layered square lattice where each layer has a different set of horizontal and vertical interactions. The free energy is determined exactly by the method of Pfaffian at two values of the magnetic field, H=0 and H=iπkT/2. The free energy at H=0 was first derived by Wolff et al. using the method of transfer matrix.

scholarly journals Anisotropic scaling of the two-dimensional Ising model I: the torus

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Anisotropic Scaling

We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings, as well as for the corresponding universal free energy finite-size scaling functions. Therefore, we review the dimer mapping, as well as the interplay between its topology and the different types of boundary conditions. As a central result, we show how both the finite system as well as the scaling form decay into contributions for the bulk, a characteristic finite-size part, and – if present – the surface tension, which emerges due to at least one antiperiodic boundary in the system. For the scaling limit we extend the proper finite-size scaling theory to the anisotropic case and show how this anisotropy can be absorbed into suitable scaling variables.

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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