论文标题
Linus Pauling的冰型模型与三色问题之间的联系
A connection between the Ice-type model of Linus Pauling and the three-color problem
论文作者
论文摘要
Linus Pauling提出的冰型模型以一种教义的方式接近了在低温下解释其熵的模型。我们首先提出理论上估计的低温熵，并将其与数值结果进行比较。 Then, we consider the mapping between this model and the three-colour problem, i.e.,colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of $N$ oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for $ n \ rightarrow \ infty $与lieb的精确解决方案进行了比较。
The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e.,colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of $N$ oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case $N\rightarrow \infty $ which is compared with the exact solution by Lieb.
