Critical temperatures of the three- and four-state Potts models on the kagome lattice
2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 83, no 6, 061104- p.Article in journal (Refereed) Published
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.
Condensed Matter Physics
Research subject Theoretical Physics
IdentifiersURN: urn:nbn:se:umu:diva-44393DOI: 10.1103/PhysRevE.83.061104OAI: oai:DiVA.org:umu-44393DiVA: diva2:420935
FunderSwedish Research Council, 621-2008-4449