On the asymptotics of dimers on tori

Preprint English OPEN
Kenyon, Richard W.; Sun, Nike; Wilson, David B.;
  • Subject: Mathematical Physics | 82B20

We study asymptotics of the dimer model on large toric graphs. Let $\mathbb L$ be a weighted $\mathbb{Z}^2$-periodic planar graph, and let $\mathbb{Z}^2 E$ be a large-index sublattice of $\mathbb{Z}^2$. For $\mathbb L$ bipartite we show that the dimer partition function... View more
  • References (42)
    42 references, page 1 of 5

    H. W. J. Blöte, J. L. Cardy, and M. P. Nightingale. Conformal invariance, the central charge, and universal finite-size amplitudes at criticality. Phys. Rev. Lett., 56:742-745, 1986.

    Ann. Probab., 37(5):1747-1777, 2009.

    [BP93] J. G. Brankov and V. B. Priezzhev. Critical free energy of a Möbius strip. Nuclear Phys. B, 400(1-3):633-652, 1993.

    [BS90] A. I. Bugrij and V. N. Shadura. The partition function of the 2D Ising model with magnetic fields on the boundaries and c 21 Virasoro characters. Physics Letters A, 150(3-4):171-178, 1990.

    [Car96] J. Cardy. Scaling and renormalization in statistical physics, volume 5 of Cambridge Lecture Notes in Physics. Cambridge University Press, 1996.

    [CDC13] D. Cimasoni and H. Duminil-Copin. The critical temperature for the Ising model on planar doubly periodic graphs. Electron. J. Probab., 18(44):1-18, 2013.

    [CKP01] H. Cohn, R. Kenyon, and J. Propp. A variational principle for domino tilings. J. Amer. Math. Soc., 14(2):297-346 (electronic), 2001.

    [CS99] J. H. Conway and N. J. A. Sloane. Sphere packings, lattices and groups, volume 290 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, New York, third edition, 1999. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov.

    [CSM03] R. Costa-Santos and B. M. McCoy. Finite size corrections for the Ising model on higher genus triangular lattices. J. Statist. Phys., 112(5-6):889-920, 2003.

    [EMOT81] A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi. Higher transcendental functions. Vol. II. Robert E. Krieger Publishing Co. Inc., Melbourne, Fla., 1981. Based on notes left by Harry Bateman, Reprint of the 1953 original.

  • Similar Research Results (1)
  • Metrics
Share - Bookmark