Phase transition of $q$-state clock models on heptagonal lattices

Details Phase transition of $q$-state clock models on heptagonal lattices Phase transition of $q$-state clock models on heptagonal lattices

2009-04-24

arxiv.org/abs/0904.3838v2

Phys. Rev. E 80, 011133 (2009)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 14 figures

Scientific paper

10.1103/PhysRevE.80.011133

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 $q \ge 2$. 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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