Periodic Ground States for the Potts Model with External Field and a Countable Set of Spin Values on the Cayley Tree

For the Potts model with external field and a countable set of spin values on the Cayley tree of order $$k\ge2$$ , the set of periodic ground states corresponding to normal divisors of indices 2 and 4 of the group presentation of the Cayley tree is described and the set of nonperiodic ground states is studied.

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