  The Lee-Yang circle theorem describes complex polynomials of degree $n$ in
$z$ with all their zeros on the unit circle $|z|=1$. These polynomials are
obtained by taking $z_1=...=z_n=z$ in certain multiaffine polynomials
$\Psi(z_1,...,z_n)$ which we call Lee-Yang polynomials (they do not vanish when
$|z_1|,...,|z_n|<1$ or $|z_1|,...,|z_n|>1$). We characterize the Lee-Yang
polynomials $\Psi$ in $n+1$ variables in terms of polynomials $\Phi$ in $n$
variables (those such that $\Phi(z_1,...,z_n)\ne0$ when $|z_1|,...,|z_n|<1$).
This characterization gives us a good understanding of Lee-Yang polynomials and
allows us to exhibit some new examples. In the physical situation where the
$\Psi$ are temperature dependent partition functions, we find that those $\Psi$
which are Lee-Yang polynomials for all temperatures are precisely the
polynomials with pair interactions originally considered by Lee and Yang.
