Skip to main content
SpringerLink
Log in

Conformal Limit for Dimer Models on the Hexagonal Lattice

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

In this note, we derive the asymptotical behavior of local correlation functions in dimer models on a domain of the hexagonal lattice in the continuum limit, when the size of the domain goes to infinity and the parameters of the model scale appropriately.

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

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. R. Kenyon, “Height fluctuations in the honeycomb dimer model,” Comm. Math. Phys., 281, 675–709 (2008).

    Article  MathSciNet  Google Scholar 

  2. A. Bufetov and A. Knizel, “Asymptotics of random domino tilings of rectangular Aztec diamonds,” Ann. Inst. H. Poincaré Probab. Statist., 54, No. 3, 1250–1290 (2018).

    Article  MathSciNet  Google Scholar 

  3. L. Petrov, “Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field,” Ann. Probab., 43, No. 1, 1–43 (2014).

    Article  MathSciNet  Google Scholar 

  4. W. Kasteleyn, “Graph theory and crystal physics,” In: Graph Theory and Theoretical Physics, Academic Press, London (1967), pp. 43–110.

  5. M. Fisher, “Statistical mechanics of dimers on a plane lattice,” Phys. Review, 124, No. 6, 1664–1672 (1961).

    Article  MathSciNet  Google Scholar 

  6. D. Cimasoni and N. Reshetikhin, “Dimers on surface graphs and spin structures,” Comm. Math. Phys., 275, No. 1, 187–208 (2007).

    Article  MathSciNet  Google Scholar 

  7. A. Okounkov and N. Reshetikhin, “Random skew plane partitions and the Pearcey process,” Comm. Math. Phys., 269, No. 3, 571–609 (2007).

    Article  MathSciNet  Google Scholar 

  8. R. Kenyon and A. Okounkov, “Limit shapes and the complex Burgers equation,” arXiv: math-ph/0507007.

Download references

Author information

Authors and Affiliations

  1. University of California, Berkeley, USA

    D. Keating & N. Reshetikhin

  2. St. Petersburg State University, St. Petersburg, Russia

    N. Reshetikhin

  3. KdV Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands

    N. Reshetikhin

  4. Google LLC, Mountain View, USA

    A. Sridhar

Authors
  1. D. Keating
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Reshetikhin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Sridhar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Keating.

Additional information

Dedicated to the 70th birthday of M. Semenov-Tian-Shansky

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 473, 2018, pp. 174–193.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Keating, D., Reshetikhin, N. & Sridhar, A. Conformal Limit for Dimer Models on the Hexagonal Lattice. J Math Sci 242, 701–714 (2019). https://doi.org/10.1007/s10958-019-04508-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-019-04508-2

Search

Navigation