Yang-Lee Zeros of Certain Antiferromagnetic Models

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. 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∼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 for the nearest-neighbor case. These new identities are verified numerically by computing the exact partition function for a square lattice of size 16×16. For the mean-field model, we write down the partition function for the ferromagnetic (FM) and antiferromagnetic (AFM) cases. We analytically show that at high temperatures the zeros of the AFM mean-field polynomial scale as ∼k^1/2 as well. Using a simple numerical method, we find the roots lie on certain curves (root curves), in the thermodynamic limit 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.