Some rigorous results on majority rule renormalization group transformations near the critical point

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

We consider the majority rule renormalization group transformation with two-by-two blocks for the Ising model on a two-dimensional square lattice. For three particular choices of the block spin configuration we prove that the model conditioned on the block spin configuration remains in the high-temperature phase even when the temperature is slightly below the critical temperature of the ordinary Ising model with no conditioning. We take as the definition of the infinite-volume limit an equation introduced in earlier work by the author. We use a computer to find an approximate solution of this equation and verify a condition which implies the existence of an exact solution.

Original languageEnglish (US)
Pages (from-to)15-37
Number of pages23
JournalJournal of Statistical Physics
Volume72
Issue number1-2
DOIs
StatePublished - Jul 1 1993

Keywords

  • Lattice spin system
  • majority rule
  • rigorous high-temperature phase

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Some rigorous results on majority rule renormalization group transformations near the critical point'. Together they form a unique fingerprint.

  • Cite this