Majority Rule at Low Temperatures on the Square and Triangular Lattices
arXiv:cond-mat/9605104 · doi:10.1007/BF02183615
Abstract
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.
20 pages, TeX file and 8 postscript figures. Figures are included using the epsf macros