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Phase transition of q-state clock models on heptagonal lattices

Authors
  • Seung Ki, Baek
  • Minnhagen, Petter
  • Shima, Hiroyuki
  • Kim, Beom Jun
Publication Date
Jan 01, 2009
Identifiers
DOI: 10.1103/PhysRevE.80.011133
OAI: oai:DiVA.org:umu-27691
Source
DiVA - Academic Archive On-line
Keywords
Language
English
License
Green
External links

Abstract

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 breaks the mean-field character in the bulk region, which establishes the consistency with results of clock models on boundary-free hyperbolic lattices.

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