• Corpus ID: 211011247

Combinatorics of 3D directed animals on a simple cubic lattice

@article{Nechaev2020CombinatoricsO3,
  title={Combinatorics of 3D directed animals on a simple cubic lattice},
  author={Sergei Nechaev and M. V. Tamm},
  journal={arXiv: Statistical Mechanics},
  year={2020}
}
We provide combinatorial arguments based on a two-dimensional extension of a locally-free semigroup allowing us to compute the growth rate, $\Lambda$, of the partition function $Z_N=N^{\theta}\Lambda^N$ of the $N$-particle directed animals ($N\gg 1$) on a simple cubic lattice in a three-dimensional space. Establishing the bijection between the particular configuration of the lattice animal and a class of equivalences of words in the 2D projective locally-free semigroup, we find we find $\ln… 

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