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

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 1993

Fingerprint

Majority Rule
Renormalization Group
Ising model
Ising Model
Critical point
critical point
Configuration
conditioning
Critical Temperature
configurations
Square Lattice
Conditioning
critical temperature
Approximate Solution
Exact Solution
Verify
Imply
temperature
Model

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Some rigorous results on majority rule renormalization group transformations near the critical point. / Kennedy, Thomas G.

In: Journal of Statistical Physics, Vol. 72, No. 1-2, 07.1993, p. 15-37.

Research output: Contribution to journalArticle

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