2009/04/30 by Seung Ki Baek, Petter Minnhagen, Hiroyuki Shima +1
Computer Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Condensed matter physics #Lattice (music) #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Phase (matter) #Phase boundary #Phase diagram #Phase transition #Physics #Potts model #Quantum mechanics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.80.011133
published as Phys. Rev. E 80, 011133 (2009) · 10 pages, 14 figures
openalex publication_date 2009/07/24 · arxiv created 2009/07/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.