Uniqueness for the q-state antiferromagnetic Potts model on the regular tree

12/01/2021

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We present an elementary proof for the uniqueness regime of the general q-state antiferromagnetic Potts model on the d-ary tree. The key observation is a positive association property of its boundary condition. We also obtain the exact exponential decay rate in all of the subcritical regime, and power law decay rate at the critical temperature.

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