Abstract
We study the phase diagram for Potts model on a Cayley tree with competing prolonged ternary and nearest–neighbor interactions. Recently Ganikhodjaev et al. [19] proved that the phase diagram of Potts model with competing nearest–neighbor and prolonged next-nearest–neighbor interactions contains a modulated phase, as found for similar Ising models on periodic lattices. At vanishing temperature, the phase diagram is fully determined for all values of interaction parameters. We show that the set of modulated phases has very simple structure, namely consist of phases with period 4, so called antiphase.
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Acknowledgements
The work is supported by The Scientific and Technological Research Council of Turkey-TUBITAK (Project No: 109T678).
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Ganikhodjaev, N., Temir, S., Uğuz, S., Akin, H. (2011). A Renormalization-Group Study of the Potts Model with Competing Ternary and Binary Interactions. In: Nonlinear and Complex Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0231-2_9
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DOI: https://doi.org/10.1007/978-1-4614-0231-2_9
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