Phase transition of q-state clock models on heptagonal lattices
2009 (English)In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 80, no 1, 011133- p.Article in journal (Refereed) Published
We study the q-state clock models on heptagonal lattices assigned on a negatively curved surface. We show that the system exhibits three classes of equilibrium phases; in between ordered and disordered phases, an intermediate phase characterized by a diverging susceptibility with no magnetic order is observed at every q >= 2. The persistence of the third phase for all q is in contrast with the disappearance of the counterpart phase in a planar system for small q, which indicates the significance of nonvanishing surface-volume ratio that is peculiar in the heptagonal lattice. Analytic arguments based on Ginzburg-Landau theory and generalized Cayley trees make clear that the two-stage transition in the present system is attributed to an energy gap of spin-wave excitations and strong boundary-spin contributions. We further demonstrate that boundary effects break the mean-field character in the bulk region, which establishes the consistency with results of clock models on boundary-free hyperbolic lattices.
Place, publisher, year, edition, pages
2009. Vol. 80, no 1, 011133- p.
ZERO-FIELD SUSCEPTIBILITY, CAYLEY TREE, ISING-MODEL, 2-DIMENSIONAL SYSTEMS, THERMODYNAMIC LIMIT, NEGATIVE-CURVATURE, POTTS-MODEL, SPIN, PSEUDOSPHERE, BEHAVIOR
IdentifiersURN: urn:nbn:se:kth:diva-32317DOI: 10.1103/PhysRevE.80.011133ISI: 000268616300045ScopusID: 2-s2.0-68949103544OAI: oai:DiVA.org:kth-32317DiVA: diva2:410029
FunderSwedish Research Council, 621-2002-4135
QC 201104122011-04-122011-04-122011-04-12Bibliographically approved