标题： 1D 和 2D 自旋$s$伊辛模型复温度性质之间的联系 显示英文标题

标题： A Connection Between Complex-Temperature Properties of the 1D and 2D Spin $s$ Ising Model

摘要： 尽管二维和一维伊辛模型的物理性质差异很大，但我们指出它们复温度相图之间的一个有趣联系。 我们对任意自旋$s$的一维伊辛模型进行了复温相图的精确确定，并表明在$u_s=e^{-K/s^2}$平面中（i）它由$N_{c,1D}=4s^2$个无限区域组成，这些区域由相同数量的边界曲线分隔，自由能在此处非解析；（ii）这些曲线从原点延伸到复无穷远，且在两个极限下沿角度$\theta_n = (1+2n)\pi/(4s^2)$方向排列，对于$n=0,..., 4s^2-1$；（iii）其中，有$N_{c,NE,1D}=N_{c,NW,1D}=[s^2]$条曲线位于第一和第二象限（东北和西北象限）；以及（iv）如果$s$是半整数，则在负实$u_s$轴上有一条边界曲线（线）。 我们注意到这些结果与我们在二维自旋$s$伊辛模型的分区函数零点最近计算中，进入FM相的零点弧的数量之间存在密切关系。 显示英文摘要

摘要： Although the physical properties of the 2D and 1D Ising models are quite different, we point out an interesting connection between their complex-temperature phase diagrams. We carry out an exact determination of the complex-temperature phase diagram for the 1D Ising model for arbitrary spin $s$ and show that in the $u_s=e^{-K/s^2}$ plane (i) it consists of $N_{c,1D}=4s^2$ infinite regions separated by an equal number of boundary curves where the free energy is non-analytic; (ii) these curves extend from the origin to complex infinity, and in both limits are oriented along the angles $\theta_n = (1+2n)\pi/(4s^2)$, for $n=0,..., 4s^2-1$; (iii) of these curves, there are $N_{c,NE,1D}=N_{c,NW,1D}=[s^2]$ in the first and second (NE and NW) quadrants; and (iv) there is a boundary curve (line) along the negative real $u_s$ axis if and only if $s$ is half-integral. We note a close relation between these results and the number of arcs of zeros protruding into the FM phase in our recent calculation of partition function zeros for the 2D spin $s$ Ising model.