Kim Seung-Yeon
School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-722, Korea.
Phys Rev Lett. 2004 Sep 24;93(13):130604. doi: 10.1103/PhysRevLett.93.130604. Epub 2004 Sep 23.
There exists the famous circle theorem on the Yang-Lee zeros of the ferromagnetic Ising model. However, the Yang-Lee zeros of the antiferromagnetic Ising model are much less well understood than those of the ferromagnetic model. The precise distribution of the Yang-Lee zeros of the antiferromagnetic Ising model only with nearest-neighbor interaction J on LxL square lattices is determined as a function of temperature a=e(2betaJ) (J<0), and its relation to the phase transitions is investigated. In the thermodynamic limit (L-->infinity), the distribution of the Yang-Lee zeros of the antiferromagnetic Ising model cuts the positive real axis in the complex x=e(-2betaH) plane, resulting in the critical magnetic field +/-H(c)(a), where H(c)>0 below the critical temperature a(c)=square root of 2-1. The results suggest that the value of the scaling exponent y(h) is 1 along the critical line for a<a(c).
在铁磁伊辛模型的杨 - 李零点方面存在著名的圆定理。然而，反铁磁伊辛模型的杨 - 李零点比铁磁模型的杨 - 李零点要难理解得多。仅针对具有最近邻相互作用(J)的(L×L)方形晶格上的反铁磁伊辛模型，确定其杨 - 李零点的精确分布作为温度(a = e^{(2\beta J)})（(J < 0)）的函数，并研究其与相变的关系。在热力学极限（(L\to\infty)）下，反铁磁伊辛模型的杨 - 李零点分布在复平面(x = e^{(-2\beta H)})中与正实轴相交，从而产生临界磁场(\pm H_c(a))，其中在临界温度(a_c = \sqrt{2} - 1)以下(H_c > 0)。结果表明，对于(a < a_c)，沿着临界线缩放指数(y(h))的值为(1)。
