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Archimedean ice
1. | Department of Mathematics, Aalto University, P. O. Box 11100, FI-00076 Aalto, Finland |
References:
[1] |
R. J. Baxter, "Exactly Solvable Models In Statistical Mechanics," Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1982. |
[2] |
F. Colomo and A. G. Pronko, The arctic circle revisited, in "Integrable Systems and Random Matrices," Contemp. Math., 458, Amer. Math. Soc., Providence, RI, (2008), 361-376.
doi: 10.1090/conm/458/08947. |
[3] |
J. H. Conway and J. C. Lagarias, Tilings with polyominoes and combinatorial group theory, J. Combin. Theory, Ser. A 53 (1990), 183-208.
doi: 10.1016/0097-3165(90)90057-4. |
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K. Eloranta, Diamond ice, J. Stat. Phys. 96 (1999), 1091-1109.
doi: 10.1023/A:1004644418182. |
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B. Grünbaum and G. C. Shephard, "Tilings And Patterns," W. H. Freeman and Company, New York, 1987. |
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W. Jockush, J. Propp and P. Shor, "Random domino tilings and the arctic circle Theorem," arXiv:math.CO/9801068. |
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P. Kasteleyn, The statistics of the dimer on a lattice, I. The number of dimer arrangements on a quadratic lattice, Physica 27 (1961), 1209-1225. |
[8] |
R. Kenyon, An introduction to the dimer model, in "School and Conference on Probability Theory," ICTP Lect. Notes, XVII, Abdus Salam Int. Cent. Theoret. Phys., Trieste, (2004), 267-304 (electronic). |
[9] |
E. Lieb, Residual entropy of square ice, Phys. Rev. 162 (1967), 162-172. |
[10] |
J. Propp, "Lattice structure for orientation of graphs," arXiv:math.CO/0209005. |
[11] |
W. P. Thurston, Conway's tiling groups, Am. Math. Monthly (1990) 757-773.
doi: 10.2307/2324578. |
[12] |
P. Walters, "An Introduction To Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
show all references
References:
[1] |
R. J. Baxter, "Exactly Solvable Models In Statistical Mechanics," Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1982. |
[2] |
F. Colomo and A. G. Pronko, The arctic circle revisited, in "Integrable Systems and Random Matrices," Contemp. Math., 458, Amer. Math. Soc., Providence, RI, (2008), 361-376.
doi: 10.1090/conm/458/08947. |
[3] |
J. H. Conway and J. C. Lagarias, Tilings with polyominoes and combinatorial group theory, J. Combin. Theory, Ser. A 53 (1990), 183-208.
doi: 10.1016/0097-3165(90)90057-4. |
[4] |
K. Eloranta, Diamond ice, J. Stat. Phys. 96 (1999), 1091-1109.
doi: 10.1023/A:1004644418182. |
[5] |
B. Grünbaum and G. C. Shephard, "Tilings And Patterns," W. H. Freeman and Company, New York, 1987. |
[6] |
W. Jockush, J. Propp and P. Shor, "Random domino tilings and the arctic circle Theorem," arXiv:math.CO/9801068. |
[7] |
P. Kasteleyn, The statistics of the dimer on a lattice, I. The number of dimer arrangements on a quadratic lattice, Physica 27 (1961), 1209-1225. |
[8] |
R. Kenyon, An introduction to the dimer model, in "School and Conference on Probability Theory," ICTP Lect. Notes, XVII, Abdus Salam Int. Cent. Theoret. Phys., Trieste, (2004), 267-304 (electronic). |
[9] |
E. Lieb, Residual entropy of square ice, Phys. Rev. 162 (1967), 162-172. |
[10] |
J. Propp, "Lattice structure for orientation of graphs," arXiv:math.CO/0209005. |
[11] |
W. P. Thurston, Conway's tiling groups, Am. Math. Monthly (1990) 757-773.
doi: 10.2307/2324578. |
[12] |
P. Walters, "An Introduction To Ergodic Theory," Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
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