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摘要翻译：
本文研究了Ising模型在复杂（能量/温度）因变量$u=e^{-4k}$平面上的一些性质，其中$k=j/(k_BT)$,对于非零外磁场，$H$。给出了该模型在一维和无限长准一维条带上在$u$平面上的相图的精确结果。在实$h=h/(k_BT)$的情况下，这些结果为我们先前对这种情况的研究提供了新的见解。我们还考虑了复数$h=h/(k_BT)$和$\mu=e^{-2h}$。本文给出了正方形格子截面上配分函数的复-$u$0的计算。对于虚的$H$，即$\mu=e^{i\theta}$的情况，我们利用准一维条带的精确结果和二维模型的配分函数零点来推断$u$平面上所得相图的一些性质。我们发现，在这种情况下，相界${\cal B}_u$包含一条穿过部分物理铁磁区间$0\leu\le1$的实线段，其右端点$u_{rhe}$位于$\mu=e^{\pm i\theta}$处，杨李边奇点出现的温度为$\mu=e^{\pm i\theta}$。利用共形场论参数将u_{rhe}$处的奇点与Yan-Lee边联系起来。
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英文标题：
《On Properties of the Ising Model for Complex Energy/Temperature and
Magnetic Field》
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作者：
Victor Matveev and Robert Shrock
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We study some properties of the Ising model in the plane of the complex (energy/temperature)-dependent variable $u=e^{-4K}$, where $K=J/(k_BT)$, for nonzero external magnetic field, $H$. Exact results are given for the phase diagram in the $u$ plane for the model in one dimension and on infinite-length quasi-one-dimensional strips. In the case of real $h=H/(k_BT)$, these results provide new insights into features of our earlier study of this case. We also consider complex $h=H/(k_BT)$ and $\mu=e^{-2h}$. Calculations of complex-$u$ zeros of the partition function on sections of the square lattice are presented. For the case of imaginary $h$, i.e., $\mu=e^{i\theta}$, we use exact results for the quasi-1D strips together with these partition function zeros for the model in 2D to infer some properties of the resultant phase diagram in the $u$ plane. We find that in this case, the phase boundary ${\cal B}_u$ contains a real line segment extending through part of the physical ferromagnetic interval $0 \le u \le 1$, with a right-hand endpoint $u_{rhe}$ at the temperature for which the Yang-Lee edge singularity occurs at $\mu=e^{\pm i\theta}$. Conformal field theory arguments are used to relate the singularities at $u_{rhe}$ and the Yang-Lee edge.
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PDF链接：
https://arxiv.org/pdf/711.4639
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