A connection between the ice-type model of Linus Pauling and the three-color problem. (20th January 2021)

• Record Type: Journal Article
• Authors: da Silva, Roberto; Nakao, Osvaldo S; de Felício, J R Drugowich
• Is Part Of: European journal of physics. Volume 42:Number 2(2021)
• Publication Date: 2021-01-20
• Subjects: ice-type model -- transfer-matrix method -- graph colouring -- didatic alternatives in statistical physics; Physics -- Periodicals; Physics -- Study and teaching (Higher) -- Europe -- Periodicals; 530
• DOI: 10.1088/1361-6404/abc89f
• Languages: English
• ISSNs: 0143-0807

Abstract

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 → ∞ which is compared with the exact solution by Lieb.