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arXiv · 1703.09340

Exact enumeration of self-avoiding walks on BCC and FCC lattices

Raoul D. Schram·Gerard T. Barkema·Rob H. Bisseling·Nathan Clisby
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Abstract

Self-avoiding walks on the body-centered-cubic (BCC) and face-centered-cubic (FCC) lattices are enumerated up to lengths 28 and 24, respectively, using the length-doubling method. Analysis of the enumeration results yields values for the exponents $\gamma$ and $\nu$ which are in agreement with, but less accurate than those obtained earlier from enumeration results on the simple cubic lattice. The non-universal growth constant and amplitudes are accurately determined, yielding for the BCC lattice $\mu=6.530520(20)$, $A=1.1785(40)$, and $D=1.0864(50)$, and for the FCC lattice $\mu=10.037075(20)$, $A=1.1736(24)$, and $D=1.0460(50)$.

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Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling, Nathan Clisby. 2017-03-27. Exact enumeration of self-avoiding walks on BCC and FCC lattices. https://doi.org/10.1088/1742-5468/aa819f

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