dorsal/arxiv
View SchemaCalculation of the Critical Temperature for 2- and 3-Dimensional Ising Models and for 2-Dimensional Potts Models Using the Transfer Matrix Method
| Authors | M. Ghaemi, G. A. Parsafar, M. Ashrafizaadeh |
|---|---|
| Categories | |
| ArXiv ID | physics/0406135 |
| URL | https://arxiv.org/abs/physics/0406135 |
| Journal | J.Phys.Chem. B105 (2001) 10355-10359 |
Abstract
A new graphical method is developed to calculate the critical temperature of 2- and 3-dimensional Ising models as well as that of the 2-dimensional Potts models. This method is based on the transfer matrix method and using the limited lattice for the calculation. The reduced internal energy per site has been accurately calculated for different 2-D Ising and Potts models using different size-limited lattices. All calculated energies intersect at a single point when plotted versus the reduced temperature. The reduced temperature at the intersection is 0.4407, 0.2746, and 0.6585 for the square, triangular, and honeycombs Ising lattices and 1.0050, 0.6309, and 1.4848 for the square, triangular, and honeycombs Potts lattices, respectively. These values are exactly the same as the critical temperatures reported in the literature, except for the honeycomb Potts lattice. For the two-dimensional Ising model, we have shown that the existence of such an intersection point is due to the duality relation. The method is then extended to the simple cubic Ising model, in which the intersection point is found to be dependent on the lattice sizes. We have found a linear relation between the lattice size and the intersection point. This relation is used to obtain the critical temperature of the unlimited simple cubic lattice. The obtained result, 0.221(2), is in a good agreement with the accurate value of 0.22165 reported by others.
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"abstract": "A new graphical method is developed to calculate the critical temperature of\n2- and 3-dimensional Ising models as well as that of the 2-dimensional Potts\nmodels. This method is based on the transfer matrix method and using the\nlimited lattice for the calculation. The reduced internal energy per site has\nbeen accurately calculated for different 2-D Ising and Potts models using\ndifferent size-limited lattices. All calculated energies intersect at a single\npoint when plotted versus the reduced temperature. The reduced temperature at\nthe intersection is 0.4407, 0.2746, and 0.6585 for the square, triangular, and\nhoneycombs Ising lattices and 1.0050, 0.6309, and 1.4848 for the square,\ntriangular, and honeycombs Potts lattices, respectively. These values are\nexactly the same as the critical temperatures reported in the literature,\nexcept for the honeycomb Potts lattice. For the two-dimensional Ising model, we\nhave shown that the existence of such an intersection point is due to the\nduality relation. The method is then extended to the simple cubic Ising model,\nin which the intersection point is found to be dependent on the lattice sizes.\nWe have found a linear relation between the lattice size and the intersection\npoint. This relation is used to obtain the critical temperature of the\nunlimited simple cubic lattice. The obtained result, 0.221(2), is in a good\nagreement with the accurate value of 0.22165 reported by others.",
"arxiv_id": "physics/0406135",
"authors": [
"M. Ghaemi",
"G. A. Parsafar",
"M. Ashrafizaadeh"
],
"categories": [
"physics.chem-ph"
],
"journal_ref": "J.Phys.Chem. B105 (2001) 10355-10359",
"title": "Calculation of the Critical Temperature for 2- and 3-Dimensional Ising Models and for 2-Dimensional Potts Models Using the Transfer Matrix Method",
"url": "https://arxiv.org/abs/physics/0406135"
},
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