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arXiv · 2006.08330

A connection between the Ice-type model of Linus Pauling and the three-color problem

R. da Silva·O. S. Nakao·J. R. Drugowich de Felício
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Abstract

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.

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R. da Silva, O. S. Nakao, J. R. Drugowich de Felício. 2020-06-07. A connection between the Ice-type model of Linus Pauling and the three-color problem. https://doi.org/10.1088/1361-6404/abc89f

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