In statistical mechanics, the Lee–Yang theorem states that if partition functions of certain models in statistical field theory with ferromagnetic interactions are considered as functions of an external field, then all zeros are purely imaginary (or on the unit circle after a change of variable).
Simon & Griffiths (1973) extended the Lee–Yang theorem to certain continuous probability distributions by approximating them by a superposition of Ising models.
Along the formalization in Newman (1974) the Hamiltonian is given by where Sj's are spin variables, zj external field.
The Lee–Yang theorem states that if the Hamiltonian is ferromagnetic and all the measures dμj have the Lee-Yang property, and all the numbers zj have positive real part, then the partition function is non-zero.
With this change of variable the Lee–Yang theorem says that all zeros ρ lie on the unit circle.