title: Phase transition of q-state clock models on heptagonal lattices.
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>or=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.
authors: Department of Physics, Umeå University, 901 87 Umeå, Sweden.
authors: Seung Ki
authors: SK
authors: Baek
authors: Petter
authors: P
authors: Minnhagen
authors: Hiroyuki
authors: H
authors: Shima
authors: Beom Jun
authors: BJ
authors: Kim