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Majority rule at low temperatures on the square and triangular lattices (1997)
| Venue: | J. Stat. Phys |
| Citations: | 6 - 0 self |
BibTeX
@ARTICLE{Kennedy97majorityrule,
author = {Tom Kennedy},
title = {Majority rule at low temperatures on the square and triangular lattices},
journal = {J. Stat. Phys},
year = {1997},
pages = {86--1089}
}
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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 [17], 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.
