Non-rotational invariance of the subcritical FK Wulff shape

Prove that the exceptional set RotFK of subcritical FK-percolation parameters at which the Wulff shape is a Euclidean sphere is empty for every dimension d\ge 2 and cluster weight q\ge 1.

Background

Theorem 1.7 proves that, away from the endpoints of the subcritical interval, only finitely many parameters can yield a rotationally invariant Wulff shape. The authors identify the stronger expected conclusion that no subcritical parameter has this rotational invariance, defining the exceptional set RotFK accordingly. They explicitly state that their method does not establish this stronger result, although it is known for the two-dimensional Ising model.