The partition function and correlation functions of the Ising model on a diamond  fractal lattices

The combinatorial approach to the triangular Ising model is shown to be considerably simplified at a given temperature TD. This enables the partition function and spin-correlation functions to be evaluated without the use of pfaffians, thus providing a simple derivation of a few of the results obtained previously by Stephenson. We confirm the results of Stephenson, that at the temperature TD, the correlation functions have the same structure as the correlations of a one-dimensional Ising lattice. The only new result is a general expression for some of the spin–spin correlation functions when the spins do not lie on the axes of the lattice.

Download Full-text

Partition function zeros for the two-dimensional Ising model

Physica A Statistical Mechanics and its Applications ◽

10.1016/0378-4371(84)90028-1 ◽

1984 ◽

Vol 129 (1) ◽

pp. 201-210 ◽

Cited By ~ 34

Author(s):

John Stephenson ◽

Rodney Couzens

Keyword(s):

Ising Model ◽

Partition Function ◽

Two Dimensional ◽

Partition Function Zeros ◽

Function Zeros

Download Full-text

Correlation functions of the one-dimensional random-field Ising model at zero temperature

Physical Review B ◽

10.1103/physrevb.48.9508 ◽

1993 ◽

Vol 48 (13) ◽

pp. 9508-9514 ◽

Cited By ~ 7

Author(s):

Edward Farhi ◽

Sam Gutmann

Keyword(s):

Ising Model ◽

Random Field ◽

Correlation Functions ◽

Zero Temperature ◽

Random Field Ising Model ◽

One Dimensional ◽

The One

Download Full-text

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

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0713 ◽

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.

Download Full-text