Spin-flip symmetry of the Lee–Yang polynomial

DefinitionGlobal spin flip#✓fully proved

The global spin flip σ ↦ -σ.

def leeYangFlip (s : ConfigSpace V) : ConfigSpace V := fun x => !(s x)

Uses 1 · Used by 3

Statement usesConfiguration space of a statistical-mechanics model

Used byGlobal spin flip as an involutive equivalence · Lee–Yang circle theorem · Ferromagnetic Lee–Yang polynomial has no zero in the open unit disk

DefinitionGlobal spin flip as an involutive equivalence#✓fully proved

The global spin flip as an involutive equivalence of configurations.

def leeYangFlipEquiv : ConfigSpace V ≃ ConfigSpace V where
  toFun := leeYangFlip
  invFun := leeYangFlip
  left_inv := leeYangFlip_involutive
  right_inv := leeYangFlip_involutive

Uses 2 · Used by 2

Statement usesConfiguration space of a statistical-mechanics model · Global spin flip

Used byLee–Yang circle theorem · Ferromagnetic Lee–Yang polynomial has no zero in the open unit disk

2 fully proved

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