Renormalization-group theory of the Heisenberg model in d dimensions

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Tunca E., Berker A. N.

Physica A: Statistical Mechanics and its Applications, vol.608, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 608
  • Publication Date: 2022
  • Doi Number: 10.1016/j.physa.2022.128300
  • Journal Name: Physica A: Statistical Mechanics and its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Artic & Antarctic Regions, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Keywords: Free energy, Internal energy, Phase transitions, Renormalization-group theory, Specific heat, Spin models
  • Open Archive Collection: AVESIS Open Access Collection
  • Istanbul University Affiliated: Yes

Abstract

© 2022 Elsevier B.V.The classical Heisenberg model has been solved in spatial d dimensions, exactly in d=1 and by the Migdal–Kadanoff approximation in d>1, by using a Fourier–Legendre expansion. The phase transition temperatures, the energy densities, and the specific heats are calculated in arbitrary dimension d. Fisher's exact result is recovered in d=1. The absence of an ordered phase, conventional or algebraic (in contrast to the XY model yielding an algebraically ordered phase) is recovered in d=2. A conventionally ordered phase occurs at d>2. This method opens the way to complex-system calculations with Heisenberg local degrees of freedom.