Transfer matrix in counting problems

Roberto da Silva, Silvio R. Dahmen () and J. R. Drugowich de Felício ()
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Roberto da Silva: Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil
Silvio R. Dahmen: Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil
J. R. Drugowich de Felício: Departamento de Física, Faculdade de Filosofia, Ciências e Letras de Riberão Preto, Universidade de São Paulo, Ribeirão Preto, São Paulo, Brazil

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 03, 1-22

Abstract: The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a three-color problem. In this paper, we explicitly build the transfer matrix for the three-color problem in order to calculate the number of possible configurations for finite systems with free, periodic in one direction and toroidal boundary conditions (periodic in both directions)

Keywords: Transfer matrix; toroidal boundary conditions; ice-type model; three-color problem (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122500322

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