Van der Waerden's Colouring Theorem and Classical Spin Systems
arXiv:cond-mat/9606009 · doi:10.1142/S0217984997001134
Abstract
We find a non-invertible matrix representation for Van der Waerden's colouring theorem for two distinct colours in a one dimensional periodic lattice. Using this,an infinite one dimensional antiferromagnetic Ising system is mapped to a pseudo-ferromagnetic one, thereby relating the couplings. All this is reminiscent of renormalisation group.
Latex, 10 pages