论文标题
刚性K-Mers在平方晶格上的熵
Entropy of rigid k-mers on a square lattice
论文作者
论文摘要
使用转移矩阵技术，我们估算了等于K（命名为K-mers）的杆的气体的熵，该杆完全覆盖了一个正方形的晶格。我们的计算是使用定期和螺旋边界条件考虑了三种不同的构造的。这些构造之一，我们称之为配置文件方法，是基于Dhar和Rajesh [Phys。 Rev. E 103，042130（2021）]获得了放置在平方晶格上的非常大链的熵的下限。据我们所知，这种方法从未被用来定义转移矩阵，但事实证明非常有用，因为与使用其他方法获得的矩阵相比，它产生的矩阵具有较小的尺寸。我们的结果是从k = 2到k = 10的链条尺寸获得的，并将其与文献中已经可用的结果进行了比较。对于二聚体（$ k = 2 $），我们的结果与Ghosh等人最近调查的三聚体（$ k = 3 $）的确切结果兼容。 Rev. E 75，01115（2007）]我们的结果也是兼容的，对于Pasinetti等人[物理评论E 104，054136（2021）]在整个杆尺寸范围内获得的模拟估计值相同。我们的结果与Dhar和Rajesh [Phys提出的尺寸$ k $的函数有关熵的行为的渐近表达是一致的。 Rev. E 103，042130（2021）]对于非常大的杆（k >> 1）。
Using the transfer matrix technique, we estimate the entropy for a gas of rods of sizes equal to k (named k-mers), which cover completely a square lattice. Our calculations were made considering three different constructions, using periodical and helical boundary conditions. One of those constructions, which we call Profile Method, was based on the calculations performed by Dhar and Rajesh [Phys. Rev. E 103, 042130 (2021)] to obtain a lower limit to the entropy of very large chains placed on the square lattice. This method, so far as we know, was never used before to define the transfer matrix, but turned out to be very useful, since it produces matrices with smaller dimensions than those obtained using other approaches. Our results were obtained for chain sizes ranging from k=2 to k=10 and they are compared with results already available in the literature. In the case of dimers ($k=2$) our results are compatible with the exact result, for trimers ($k=3$), recently investigated by Ghosh et al [Phys. Rev. E 75, 011115 (2007)] also our results were compatible, the same happening for the simulational estimates obtained by Pasinetti et al [Physical Review E 104, 054136 (2021)] in the whole range of rod sizes. Our results are consistent with the asymptotic expression for the behavior of the entropy as a function of the size $k$, proposed by Dhar and Rajesh [Phys. Rev. E 103, 042130 (2021)] for very large rods (k>>1).
