Majority Rule at Low Temperatures on the Square and Triangular Lattices

Details Majority Rule at Low Temperatures on the Square and Triangular Lattices Majority Rule at Low Temperatures on the Square and Triangular Lattices

1996-05-16

arxiv.org/abs/cond-mat/9605104v1

Physics

Condensed Matter

20 pages, TeX file and 8 postscript figures. Figures are included using the epsf macros

Scientific paper

10.1007/BF02183615

We consider the majority rule renormalization group transformation applied to nearest neighbor Ising models. For the square lattice with 2 by 2 blocks we prove that if the temperature is sufficiently low, then the transformation is not defined. We use the methods of van Enter, Fernandez and Sokal, who proved the renormalized measure is not Gibbsian for 7 by 7 blocks if the temperature is too low. For the triangular lattice we prove that a zero temperature majority rule transformation may be defined. The resulting renormalized Hamiltonian is local with 14 different types of interactions.

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