Exact renormalization analysis of a self-similar phase diagram with upsilon points for an Ising model

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3 Citations (Scopus)

Abstract

The ground-state phase diagram is analyzed for a one-dimensional Ising model with long range interaction in the presence of uniform and staggered magnetic fields; the interaction is antiferromagnetic and its strength decays exponentially with distance. The exact renormalization formulas for the interactions between interfaces are derived, which is used to calculate the phase diagram hierarchically. The phase diagram is self-similar, and it contains upsilon points and devil's staircases; this agrees with the result of Aubry, Axel and Vallet [J. Phys. C 18 (1985) 753] for an equivalent, model obtained by a different method. A simple "phase rule" presenting what kind of phases appear and how they are located in the phase diagram is derived. The application of this rule to the phase diagram of betaine calcium chloride dihydrate is discussed.

Original languageEnglish
Pages (from-to)3562-3574
Number of pages13
Journaljournal of the physical society of japan
Volume68
Issue number11
DOIs
Publication statusPublished - 1999 Jan 1

Keywords

  • Devil's staircase
  • Ising model
  • Phase diagram
  • Renormalization
  • Upsilon point

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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