硬刚杆系的Bethe近似：随机局部树状层状晶格
Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice
摘要：
研究了固定长度为k的刚性长杆系统的Bethe近似，其中只排除体积相互作用。对于足够大的k，该系统经历了各向同性的相变作为密度的杆的函数。Bethe晶格，这是传统上用于推导自洽方程的Bethe近似，是不适合研究硬棒系统，因为它不允许一个密集的包装棒。我们定义了一个新的晶格，称为随机局部树状层状晶格，它允许密集包装的杆，并为近似是准确的。我们发现，对于一个4配位晶格，k>=4的k-mer经历了一个连续的相变。对于偶数配位数q>=6，跃迁只存在于k >= k_{min}（q）时，并且是一阶的.
英文摘要：
We study the Bethe approximation for a system of long rigid rods of fixed length k, with only excluded volume interaction. For large enough k, this system undergoes an isotropic-nematic phase transition as a function of density of the rods. The Bethe lattice, which is conventionally used to derive the self-consistent equations in the Bethe approximation, is not suitable for studying the hard-rods system, as it does not allow a dense packing of rods. We define a new lattice, called the random locally tree-like layered lattice, which allows a dense packing of rods, and for which the approximation is exact. We find that for a 4-coordinated lattice, k-mers with k>=4 undergo a continuous phase transition. For even coordination number q>=6, the transition exists only for k >= k_{min}(q), and is first order.
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