Majority rule at low temperatures on the square and triangular lattices

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4 Scopus citations


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, Fernández, 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.

Original languageEnglish (US)
Pages (from-to)1089-1107
Number of pages19
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Mar 1997


  • Majority-rule renormalization-group transformation
  • Non-Gibbsian measures

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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