| Autor: |
Sedik M; Physics Department, University of California, Santa Cruz, California 95064, USA., Bhat JM; International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560 089, India., Dhar A; International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560 089, India., Shastry BS; Physics Department, University of California, Santa Cruz, California 95064, USA. |
| Jazyk: |
angličtina |
| Zdroj: |
Physical review. E [Phys Rev E] 2024 Jul; Vol. 110 (1-1), pp. 014117. |
| DOI: |
10.1103/PhysRevE.110.014117 |
| Abstrakt: |
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 ∼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 identities are verified numerically by computing the exact partition function for a two-dimensional square lattice of size 16×16. 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 ∼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 nonzero complex staggered magnetization, and thus depict a complex phase boundary. |
| Databáze: |
MEDLINE |
| Externí odkaz: |
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