A connection between the ice-type model of Linus Pauling and the three-color problem
Visualizar/abrir
Data
2021Tipo
Assunto
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 twodimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurat ...
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 twodimensional 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. ...
Contido em
European Journal of Physics. Bristol. Vol. 42, no. 2 (Mar. 2021), 025101, 20 p.
Origem
Estrangeiro
Coleções
-
Artigos de Periódicos (39074)Ciências Exatas e da Terra (5943)
Este item está licenciado na Creative Commons License