Real-space renormalization group for the transverse-field Ising model in two and three dimensions

Ryoji Miyazaki, Hidetoshi Nishimori, Gerardo Ortiz

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.

Original languageEnglish
Article number051103
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume83
Issue number5
DOIs
Publication statusPublished - 2011 May 2

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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