简单立方格子上三维有向动物的组合学

Sergei Nechaev; Michael Tamm

简单立方格子上三维有向动物的组合学

统计力学 2020-09-22 v2 高能物理 - 理论组合数学

作者: Sergei Nechaev , Michael Tamm

摘要

我们提供了基于局部自由半群的二维扩展的组合论证，使得能够计算三维空间中简单立方格子上 $N$ 粒子有向动物（ $N\gg 1$ ）的配分函数 $Z_N=N^{\theta}\Lambda^N$ 的增长率 $\Lambda$ 。通过建立格子动物的特定构型与二维射影局部自由半群中词等价类之间的双射，我们发现 $\ln \Lambda = \lim_{N\to\infty} \ln Z_N / N$ ，其中 $\Lambda= 2(\sqrt{2}+1) \approx 4.8284$ 。

关键词

有向动物简单立方格子增长率配分函数局部自由半群组合学双射

引用

@article{arxiv.2002.00618,
  title  = {Combinatorics of 3D directed animals on a simple cubic lattice},
  author = {Sergei Nechaev and Michael Tamm},
  journal= {arXiv preprint arXiv:2002.00618},
  year   = {2020}
}

备注

We have realized that "Mikado ordering" valid in 2D fails in 3D. We found source of error and have proposed a new approach for enumeration of 3D heaps of pieces based on a nontrivial relation to the 2D hard-core lattice gas. We would like to withdraw the paper because the replacement could be confusing: we do not make modifications of a former approach, but replace it with a principally new one

简单立方格子上三维有向动物的组合学

摘要

关键词

引用

备注

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