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F. Spitzer (1958) [doi:https://doi.org/10.1090/S0002-9947-1958-0104296-5]
1958
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R. J. Baxter, S. B. Kelland, F. Y. Wu (1976) [doi:10.1088/0305-4470/9/3/009]
1976
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B. Nienhuis (1982) [doi:10.1103/PhysRevLett.49.1062]
1982
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H. Saleur (1986) New exact critical exponents for 2d self avoiding walks
1986
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B. Duplantier, H. Saleur (1988) [doi:10.1103/PhysRevLett.60.2343]
1988
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B. Duplantier (1988) [doi:https://doi.org/10.1007/BF01019770]
1988
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G. W. Moore, N. Seiberg (1989) [doi:10.1007/BF01238857]
1989
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L. Schäfer, C. von Ferber, U. Lehr, B. Duplantier (1992) [doi:https://doi.org/10.1016/0550-3213(92)90397-T]
1992
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B. Duplantier, I. A. Binder (2002) [doi:10.1103/PhysRevLett.89.264101]
2002
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J. Fuchs, I. Runkel, C. Schweigert (2002) [arXiv:hep-th/0204148] [doi:10.1016/S0550-3213(02)00744-7]
2002
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J. L. Jacobsen, S. Ribault, H. Saleur (2022) [arXiv:2208.14298] Spaces of states of the two-dimensional O(n) and Potts models
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2022
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L. Grans-Samuelsson, R. Nivesvivat, J. L. Jacobsen, S. Ribault, H. Saleur (2022) [arXiv:2111.01106] [doi:10.21468/SciPostPhys.12.5.147]
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2022
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2023

From combinatorial maps to correlation functions in loop models

Grans-Samuelsson, Linnea, Jacobsen, Jesper Lykke, Nivesvivat, Rongvoram et al.

Understand

In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops.

We define sums associated to a large class of combinatorial maps (also known as ribbon graphs).
We allow disconnected maps, but not maps that include monogons.
Given a map with n vertices, we obtain a function of the moduli of the corresponding punctured Riemann surface.

Built on

F. Spitzer (1958) [doi:https://doi.org/10.1090/S0002-9947-1958-0104296-5]
1958
Earlier work this paper cites.
R. J. Baxter, S. B. Kelland, F. Y. Wu (1976) [doi:10.1088/0305-4470/9/3/009]
1976
Earlier work this paper cites.
B. Nienhuis (1982) [doi:10.1103/PhysRevLett.49.1062]
1982
Earlier work this paper cites.
H. Saleur (1986) New exact critical exponents for 2d self avoiding walks
1986
Earlier work this paper cites.
B. Duplantier, H. Saleur (1988) [doi:10.1103/PhysRevLett.60.2343]
1988
Earlier work this paper cites.
B. Duplantier (1988) [doi:https://doi.org/10.1007/BF01019770]
1988
Earlier work this paper cites.
G. W. Moore, N. Seiberg (1989) [doi:10.1007/BF01238857]
1989
Earlier work this paper cites.
L. Schäfer, C. von Ferber, U. Lehr, B. Duplantier (1992) [doi:https://doi.org/10.1016/0550-3213(92)90397-T]
1992
Earlier work this paper cites.
B. Duplantier, I. A. Binder (2002) [doi:10.1103/PhysRevLett.89.264101]
2002
Earlier work this paper cites.
J. Fuchs, I. Runkel, C. Schweigert (2002) [arXiv:hep-th/0204148] [doi:10.1016/S0550-3213(02)00744-7]
2002
Earlier work this paper cites.