论文标题
$ d $ d $维型晶格的完全挤满硬硬杆的熵
Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices
论文作者
论文摘要
我们确定$ k \ times $ k \ times 1 $和$ 1 \ times k $的$ l \ times m $ square晶格的熵的渐进性行为，以$ k $的极限为准。我们表明，只有在$ l $和$ m $中的至少一个是$ k $的倍数的情况下，才有可能的覆盖范围，并且可以从所有杆的标准配置中达到所有允许的配置，仅使用$ k \ times k \ times k $ k $ a $ k $ k $ a $ k $ a $ k $ a $ k $ a $ k $ a $ k $ a $ k $ a $ k $ a $ k $ a $ k $。在大型$ k $的限制下，我们表明每个站点$ s_2（k）$倾向于$ a k^{ - 2} \ ln k $，$ a = 1 $。我们根据扰动的系列扩展的猜想，每个站点的熵的熵行为是超额的，并且继续保留所有$ d $ d $ d $二维的超基因晶格，并带有$ d \ geq 2 $。
We determine the asymptotic behavior of the entropy of full coverings of a $L \times M$ square lattice by rods of size $k\times 1$ and $1\times k$, in the limit of large $k$. We show that full coverage is possible only if at least one of $L$ and $M$ is a multiple of $k$, and that all allowed configurations can be reached from a standard configuration of all rods being parallel, using only basic flip moves that replace a $k \times k$ square of parallel horizontal rods by vertical rods, and vice versa. In the limit of large $k$, we show that the entropy per site $S_2(k)$ tends to $ A k^{-2} \ln k$, with $A=1$. We conjecture, based on a perturbative series expansion, that this large-$k$ behavior of entropy per site is super-universal and continues to hold on all $d$-dimensional hyper-cubic lattices, with $d \geq 2$.
