  We revisit the somewhat less studied problem of Yang-Lee zeros of the Ising
antiferromagnet. For this purpose, we study two models, the nearest-neighbor
model on a square lattice, and the more tractable mean-field model
corresponding to infinite-ranged coupling between all sites. In the
high-temperature limit, we show that the logarithm of the Yang-Lee zeros can be
written as a series in half odd integer powers of the inverse temperature, $k$,
with the leading term $\sim k^{1/2}$. This result is true in any dimension and
for arbitrary lattices. We also show that the coefficients of the expansion
satisfy simple identities (akin to sum rules) for the nearest-neighbor case.
These new identities are verified numerically by computing the exact partition
function for a 2D square lattice of size $16\times16$. For the mean-field
model, we write down the partition function (termed the mean-field polynomials)
for the ferromagnetic (FM) and antiferromagnetic (AFM) cases, and derive from
them the mean-field equations. We analytically show that at high temperatures
the zeros of the AFM mean-field polynomial scale as $\sim k^{1/2}$ as well.
Using a simple numerical method, we find the roots lie on certain curves (the
root curves), in the thermodynamic limit for the mean-field polynomials for the
AFM case as well as for the FM one. Our results show a new root curve, that was
not found earlier. Our results also clearly illustrate the phase transition
expected for the FM and AFM cases, in the language of Yang-Lee zeros. Moreover,
for the AFM case, we observe that the root curves separate two distinct phases
of zero and non-zero complex staggered magnetization, and thus depict a complex
phase boundary.
