Antiferroelectric transition in β-alumina, a realization of the D = 2, s = 3 Potts model ?

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Abstract
A model based on electric dipole-dipole interactions is proposed to explain the recently observed ordering transition in stoichiometric silver β-alumina. The low temperature phase is a three-fold degenerate antiferroelectric array of dipoles associated with Ag + and O- -5 ions. When T → T c with (T - Tc)/Tc > 10 -2, the correlation length ξ increases in the D = 2 layers with a critical behaviour ξ ∼ (T — Tc) -ν which is supposed to belong to the D = 2, s = 3 Potts model universality class : we find νexp = 0.85 ± 0.1 as ν th ∼ 0.83