Abstract
We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on strip graphs G of the honeycomb lattice for a variety of transverse widths equal to L y vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form \(Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}}c_{Z,G,j}(\lambda_{Z,G,j})^{m}\) , where m denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for N Z,G,j for arbitrary L y . We also present plots of zeros of the partition function in the q plane for various values of v and in the v plane for various values of q. Plots of specific heat for infinite-length strips are also presented, and, in particular, the behavior of the Potts antiferromagnet at \(q=(3+\sqrt{5}\ )/2\) is investigated.
Similar content being viewed by others
References
Fortuin, C.M., Kasteleyn, P.W.: Physica 57, 536 (1972)
Bollobás, B.: Modern Graph Theory. Springer, New York (1998)
Salas, J., Sokal, A.D.: J. Stat. Phys. 86, 551 (1997)
Shrock, R., Tsai, S.-H.: J. Phys. A 30, 495 (1997)
Wu, F.Y.: Rev. Mod. Phys. 54, 235 (1982)
Baxter, R.J.: Exactly Solved Models in Statistical Mechanics. Academic Press, London (1982)
Richard, J.-F., Jacobsen, J.L.: Nucl. Phys. B 731, 335 (2005)
Jacobsen, J.L., Saleur, H.: Nucl. Phys. B 743, 207 (2006)
Chang, S.-C., Shrock, R.: Physica A 296, 183 (2001)
Salas, J., Sokal, A.: J. Stat. Phys. 104, 609 (2001)
Chang, S.-C., Shrock, R.: Physica A 296, 131 (2001)
Chang, S.-C., Salas, J., Shrock, R.: J. Stat. Phys. 107, 1207 (2002)
Chang, S.-C., Jacobsen, J., Salas, J., Shrock, R.: J. Stat. Phys. 114, 763 (2004)
Chang, S.-C., Shrock, R.: arXiv:cond-mat/0703014 (2007)
Kim, D., Joseph, R.: J. Phys. C 7, L167 (1974)
Burkhardt, T.W., Southern, B.W.: J. Phys. A 11, L247 (1978)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, SC., Shrock, R. Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice. J Stat Phys 130, 1011–1024 (2008). https://doi.org/10.1007/s10955-007-9461-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-007-9461-3