Phase transition of q-state clock models on heptagonal lattices

Seung Ki Baek, Petter Minnhagen, Hiroyuki Shima, and Beom Jun Kim
Phys. Rev. E 80, 011133 – Published 24 July 2009

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 q2. 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.

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  • Received 23 April 2009

DOI:https://doi.org/10.1103/PhysRevE.80.011133

©2009 American Physical Society

Authors & Affiliations

Seung Ki Baek1, Petter Minnhagen1, Hiroyuki Shima2, and Beom Jun Kim3,4,*

  • 1Department of Physics, Umeå University, 901 87 Umeå, Sweden
  • 2Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
  • 3BK21 Physics Research Division and Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea
  • 4Department of Computational Biology, School of Computer Science and Communication, Royal Institute of Technology, 100 44 Stockholm, Sweden

  • *Corresponding author; beomjun@skku.edu

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Issue

Vol. 80, Iss. 1 — July 2009

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