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Periodic and weakly periodic ground states for the Potts model with competing interactions on the Cayley tree

Abstract

We consider the Potts model with competing interactions on the Cayley tree of order k with k ≥ 2. We describe the sets of periodic and weakly periodic ground states corresponding to normal subgroups of the group representation of the Cayley tree of index 4.

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Correspondence to M. M. Rakhmatullaev.

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Original Russian Text © M.M. Rakhmatullaev and M.A. Rasulova, 2015, published in Matematicheskie Trudy, 2015, Vol. 18, No. 2, pp. 112–132.

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Rakhmatullaev, M.M., Rasulova, M.A. Periodic and weakly periodic ground states for the Potts model with competing interactions on the Cayley tree. Sib. Adv. Math. 26, 215–229 (2016). https://doi.org/10.3103/S1055134416030056

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Keywords

  • Cayley tree
  • Potts model
  • periodic and weakly periodic ground states