Van der Waerden's Colouring Theorem and Weak-Strong Duality on the Lattice

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Van der Waerden's (VDW) colouring theorem in combinatoric number theory [1] has scope for physical applications.The solution of the two colour case has enabled the construction of an explicit mapping of an infinite, one dimensional antiferromagnetic Ising system to an effective pseudo- ferromagnetic one with the coupling constants in the two cases becoming related [2].Here the three colour problem is solved and the results are used to obtain new insights in the theory of complex lattices, particularly those relating to ternary alloys. The existence of these mappings of a multicolour lattice onto a monochromatic one with different couplings illustrates {\it a new form of duality}.
13 pages, Latex

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Condensed Matter, High Energy Physics - Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/28648

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/9810030
 http://arxiv.org/abs/cond-mat/9810030

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arXiv