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

Authors :
da Silva, R.
Nakao, O. S.
de Felício, J. R. Drugowich
Source :
European Journal of Physics, 42, 025101 (2021)
Publication Year :
2020

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.<br />Comment: 25 pages, 10 figures

Details

Database :
arXiv
Journal :
European Journal of Physics, 42, 025101 (2021)
Publication Type :
Report
Accession number :
edsarx.2006.08330
Document Type :
Working Paper
Full Text :
https://doi.org/10.1088/1361-6404/abc89f