Skip to main content

An Exact Renormalisation in a Vertex Model

  • Chapter
  • 302 Accesses

Part of the book series: NATO ASI Series ((NSSB,volume 315))

Abstract

In this paper we propose a real-space renormalisation procedure for a class of homogeneous vertex models. This procedure is implemented for the 27-state model associated to a minimal irreducible representation of the quantised enveloping algebra of the exceptional Lie group E 6.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Aschbacher [1987], The 27-dimensional module for E 6, Invent. Math. 89, 159.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. J.J. Binney, N.J. Dowrick, A.J. Fisher and M.E.J. Newman [1992], “The theory of critical phenomena”, Oxford Univ. Press, New York.

    MATH  Google Scholar 

  3. J.S. Birman and H. Wenzl [1989] Braids, link polynomials and a new algebra, Trans. Am. Math. Soc. 313, 249.

    Article  MathSciNet  MATH  Google Scholar 

  4. Jimbo [1989], Introduction to the Yang-Baxter equation, in “Braid Group, Knot Theory and Statistical Mechanics”, C.N. Yang and M.L. Ge eds., Advanced Series in Mathematical Physics, vol. 9, World Scientific.

    Google Scholar 

  5. V.F.R. Jones [1987], Hecke algebra representations of braid groups and link polynomials, Ann. of Math (2) 126, 335.

    Article  MathSciNet  MATH  Google Scholar 

  6. G. Lusztig [1988], Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70, 237.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Niemeijer and J.M.J. van Leeuwen [1976], Renormalization theory for Ising-like spin systems, in “Phase Transitions and critical phenomena”, C. Domb and M.S. Green, eds., vol. 6, Academic Press, New York.

    Google Scholar 

  8. H. Wenzl [1990], Quantum groups and subfactors of type B,C,D, Comm. Math. Phys. 133, 383.

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media New York

About this chapter

Cite this chapter

Westbury, B.W. (1993). An Exact Renormalisation in a Vertex Model. In: Osborn, H. (eds) Low-Dimensional Topology and Quantum Field Theory. NATO ASI Series, vol 315. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1612-9_17

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-1612-9_17

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1614-3

  • Online ISBN: 978-1-4899-1612-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics