Local statistics of lattice dimers
Annales de l'I.H.P. Probabilités et statistiques (1997)
- Volume: 33, Issue: 5, page 591-618
- ISSN: 0246-0203
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top- [BH] H.W.J. Blöte and H.J. Hilhorst, Roughening transitions and the zerotemperature triangular Ising antiferromagnet, J. Phys. A Vol. 15, 1982, L631-L637. MR679091
- [BP] R. Burton and R. Pemantle, Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer impedances, Ann. Probab., Vol. 21, 1993, pp. 1329-1371. Zbl0785.60007MR1235419
- [C] L. Comtet , Advanced combinatorics, D. Reidel Publishing Company, Dordrecht. Zbl0283.05001MR460128
- [CEP] H. Cohn and N. Elkies, J. Propp, Local statistics for random domino tilings of the Aztec diamond, Duke Math. J., Vol. 85, 1996, pp. 117-166. Zbl0866.60018MR1412441
- [CKP] H. Cohn and R. Kenyon, J. Propp, in preparation.
- [EKLP] N. Elkies, G. Kuperberg and M. Larsen, J. Propp, Alternating sign matrices and domino tilings. J. Alg. Combinatorics, Vol. 1, 1992, pp. 111-132. Zbl0779.05009MR1226347
- [FS] M.E. Fisher and J. Stephenson, Statistical mechanics of dimers on a plane lattice II. Dimer correlations and monomers, Phys. Rev. , Vol. 132, 1963, pp. 1411-1431. Zbl0132.22304MR158705
- [HG] C.A. Hurst and H.S. Green, New solution of the Ising problem for a rectangular lattice, J. Chem. Phys., Vol. 33, 1960, pp. 1059-1062. MR116546
- [K1] P.W. Kasteleyn, The statistics of dimers on a lattice, Physica, Vol. 27, 1961, pp. 1209-1225. Zbl1244.82014
- [K2] P.W. Kasteleyn, Graph theory and crystal physics, in Graph Theory and Theoretical Physics, Academic Press, London1967. Zbl0205.28402MR253689
- [MPW] E.W. Montroll, R.B. Potts and J.C. Ward, Correlations and spontaneous magnetization of the two-dimensional Ising model, J. Math. Phys., Vol. 4, 1963, p. 308-322. MR148406
- [P] K. Petersen, Ergodic theory, Cambridge studes in advanced mathematics 2, Cambridge university press, Cambridge, 1983. Zbl0507.28010MR833286
- [PW] J. Propp and D. Wilson, in preparation.
- [St] J. Stephenson, Ising-model spin correlations on the triangular lattice, J. Math. Phys., Vol. 5, 1964, pp. 1009-1024. MR168310
- [T] W. Thurston , Conway's tiling groups, Am. Math. Monthly, Vol. 97, 1990, pp. 757-773. Zbl0714.52007MR1072815
- [TF] H. Templerley and M. Fisher, The dimer problem in statistical mechanics - an exact result. Phil Mag., Vol. 6, 1961, pp. 1061-1063. Zbl0126.25102MR136398
- [W] T. Wu, Dimers on rectangular lattices, J. Math. Phys, Vol. 3, 1962, pp. 1265-1266. Zbl0113.23406MR149896