Skip to main content
SpringerLink
Log in

Real-space renormalization group approach of the Potts model on the octagonal quasi-periodic tiling

  • Published:
Wuhan University Journal of Natural Sciences

Abstract

A one-step real-space renormalization group (RSRG) transformation is used to study the ferromagnetic (FM) Potts model on the two-dimensional (2D) octagonal quasi-periodic tiling (OQT). The critical exponents of the correlation length in theq=1,2,3,4 cases and the crtitical surface of the Ising model are obtained. The results are discussed by comparing with previous results on the OQT and the square lattice (SQL).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Onsager L. Crystal statistics I: a two-dimensional model with an order-disorder transition.Phys Rev, 1944,65:117

    Article  MATH  MathSciNet  Google Scholar 

  2. Shechtman D. Metallic phase with long-range orientational order and no translational symmetry.Phys Rev Lett, 1984,53:1951

    Article  Google Scholar 

  3. Sorensen E S. Ising model on Penrose lattices: boundary conditions.Phys Rev, 1991,B44:9271

    Google Scholar 

  4. Doroba A. Equivalence of the Ising model on the two-dimensional Penrose and two-dimensional regular lattice.Acta Physica Pol, 1989,A76:949

    MathSciNet  Google Scholar 

  5. Ledue D. Static critical behavior of the ferromagnetic Ising model on the quasiperiodic octagonal tiling.Phys Rev, 1995,B51:12523

    Google Scholar 

  6. Ledue D. Static critical behavior of a weakly-frustrated Ising model on the octagonal tiling.Phys Rev, 1995, B53:3312

    Google Scholar 

  7. Tracy C A. Universality classes of some aperiodic Ising models.J Phys, 1988, A21:L603

    MathSciNet  Google Scholar 

  8. Wilson W G, Vause C A. Ferromagneticq=4,5 Potts Models on the two-dimensional Penrose and square lattices.Phys Rev, 1989, B39:4651

    Article  Google Scholar 

  9. Sire C, Bellisard J. Renormalization group for the octagonal quasi-periodic tiling.Europhys Lett, 1990,11: 439

    Article  Google Scholar 

  10. Tsallis C, de Magalhaes A C N. Pure and random Potts-like models.Phys Rept, 1996,268:305

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Wuhan University, 430072, Wuhan, China

    Xiong Gang, Zhang Zhehua & Tian Decheng

Authors
  1. Xiong Gang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhang Zhehua
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tian Decheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the National Natural Science Foundation of China (No. 19334011-C)

Xiong Gang: born in 1973, Ph.D graduate student

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gang, X., Zhehua, Z. & Decheng, T. Real-space renormalization group approach of the Potts model on the octagonal quasi-periodic tiling. Wuhan Univ. J. Nat. Sci. 3, 293–296 (1998). https://doi.org/10.1007/BF02829977

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02829977

Key words

Search

Navigation