TY - JOUR
T1 - Exact potts model partition functions for strips of the honeycomb lattice
AU - Chang, Shu Chiuan
AU - Shrock, Robert
N1 - Funding Information:
Acknowledgements This research was partially supported by the Taiwan NSC grant NSC-95-2112-M-006-004 and NSC-95-2119-M-002-001 (S.-C.C.) and the US NSF grant PHY-03-54776 (R.S.).
PY - 2008/3
Y1 - 2008/3
N2 - 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)=∑j=1NZ,G,λ cZ,G,j (λZ,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+√5)\2 is investigated.
AB - 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)=∑j=1NZ,G,λ cZ,G,j (λZ,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+√5)\2 is investigated.
UR - http://www.scopus.com/inward/record.url?scp=38349036293&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38349036293&partnerID=8YFLogxK
U2 - 10.1007/s10955-007-9461-3
DO - 10.1007/s10955-007-9461-3
M3 - Article
AN - SCOPUS:38349036293
SN - 0022-4715
VL - 130
SP - 1011
EP - 1024
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5
ER -