Open-boundary transverse-field Ising model admits exact invertible duality, invertible critical symmetry, and spontaneous duality breaking from differing physical sensitivities to local perturbations.
Maldacena, The large-n limit of superconformal field theories and supergravity, International journal of theo- retical physics38, 1113 (1999)
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Invertible Symmetry and Spontaneous Duality Breaking in the Transverse-Field Ising Model
Open-boundary transverse-field Ising model admits exact invertible duality, invertible critical symmetry, and spontaneous duality breaking from differing physical sensitivities to local perturbations.