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Critical temperatures of the three- and four-state Potts models on the kagome lattice
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea.
2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 83, no 6, 061104- p.Article in journal (Refereed) Published
Abstract [en]

The value of the internal energy per spin is independent of the strip widthfor a certain class of spin systems on two dimensional infinite strips. Itis verified that the Ising model on the kagome lattice belongs to this classthrough an exact transfer-matrix calculation of the internal energy for thetwo smallest widths. More generally, one can suggest an upper bound forthe critical coupling strength $K_c(q)$ for the $q$-state Potts model fromexact calculations of the internal energy for the two smallest stripwidths. Combining this with the corresponding calculation for the duallattice and using an exact duality relation enables us to conjecture thecritical coupling strengths for the three- and four-state Pottsmodels on the kagome lattice. The values are $K_c(q=3)=1.056~509~426~929~0$and $K_c(q=4) = 1.149~360~587~229~2$,and the values can, in principle, be obtained to an arbitrary precision. Wediscuss the fact that these values are in the middle of earlierapproximate results and furthermore differ from earlier conjecturesfor the exact values.

Place, publisher, year, edition, pages
American Physical Society , 2011. Vol. 83, no 6, 061104- p.
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:umu:diva-44393DOI: 10.1103/PhysRevE.83.061104OAI: oai:DiVA.org:umu-44393DiVA: diva2:420935
Funder
Swedish Research Council, 621-2008-4449
Available from: 2011-06-09 Created: 2011-06-07 Last updated: 2017-12-11Bibliographically approved

Open Access in DiVA

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