# Phase transition of q-state clock models on heptagonal lattices.

@article{Baek2009PhaseTO, title={Phase transition of q-state clock models on heptagonal lattices.}, author={Seung Ki Baek and Petter Minnhagen and Hiroyuki Shima and Beom Jun Kim}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2009}, volume={80 1 Pt 1}, pages={ 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>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…

## 7 Citations

Two-dimensional XY and clock models studied via the dynamics generated by rough surfaces.

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By comparative studies, it is found that the critical exponents of the majority-vote model on hyperbolic lattices satisfy the hyperscaling relation 2beta/nu+gamma/nu=D(eff), where D(eff) is an effective dimension of the lattice.

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It is found that the crossing probability increases gradually from 0 to 1 as p increases from the lower p_{l} to the upper p_{u} critical values, and bounds and estimates are found for the values of p l and p u for these lattices.

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