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We study the loop $O(n)$ model on the honeycomb lattice.
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2004
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Federico Camia and Charles M. Newman, Two-dimensional critical percolation: the full scaling limit , Comm. Math. Phys. 268
2006
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by same author, Towards conformal invariance of 2D lattice models , International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1421–1451. MR 2275653 (2008g:82026)
2006
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Roger S. K. Mong, David J. Clarke, Jason Alicea, Netanel H. Lindner, and Paul Fendley, Parafermionic conformal field theory on the lattice , J. Phys. A 47
2014
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Dmitry Chelkak, Clément Hongler, and Konstantin Izyurov, Conformal invariance of spin correlations in the planar Ising model , Ann. of Math. (2) 181
2015
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Alexander Glazman, Connective constant for a weighted self-avoiding walk on ℤ 2 \mathbb{Z}^{2} , Electronic Communications in Probability 20
2015
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Richard W. Kenyon and David B. Wilson, Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs , J. Amer. Math. Soc. 28
2015
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David Aasen, Roger SK Mong, and Paul Fendley, Topological defects on the lattice: I. the Ising model , Journal of Physics A: Mathematical and Theoretical 49
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Y. Ikhlef and J.L. Cardy, Discretely holomorphic parafermions and integrable loop models , J. Phys. A 42
2009
Cited alongside, same era.
C. Hongler, Conformal invariance of Ising model correlations , Ph.D. thesis, université de Genève, 2010, p. 118
2010
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Giuseppe Mussardo, Statistical field theory , Oxford Graduate Texts, Oxford University Press, Oxford, 2010, An introduction to exactly solved models in statistical physics. MR 2559725 (2010k:82001)
2010
Cited alongside, same era.
by same author, Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model , Ann. of Math. (2) 172
2010
Cited alongside, same era.
by same author, Discrete complex analysis and probability , Proceedings of the International Congress of Mathematicians. Volume I (New Delhi), Hindustan Book Agency, 2010, pp. 595–621. MR 2827906
2010
Cited alongside, same era.
Dmitry Chelkak and Stanislav Smirnov, Discrete complex analysis on isoradial graphs , Adv. Math. 228
2011
Cited alongside, same era.
H. Duminil-Copin, C. Hongler, and P. Nolin, Connection probabilities and RSW-type bounds for the two-dimensional FK Ising model , Comm. Pure Appl. Math. 64
2011
Cited alongside, same era.
2016
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Vincent Tassion, Crossing probabilities for Voronoi percolation , Ann. Probab. 44
2016
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Dmitry Chelkak, David Cimasoni, and Adrien Kassel, Revisiting the combinatorics of the 2D Ising model , Annales de l’Institut Henri Poincaré D 4
2017
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Hugo Duminil-Copin, Ron Peled, Wojciech Samotij, and Yinon Spinka, Exponential decay of loop lengths in the loop O ( n ) O(n) model with large n n , Comm. Math. Phys. 349
2017
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S. Friedli and Y. Velenik, Statistical mechanics of lattice systems: a concrete mathematical introduction , Cambridge University Press, 2017
2017
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Antti Kemppainen and Stanislav Smirnov, Random curves, scaling limits and Loewner evolutions , The Annals of Probability 45
2017
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Dmitry Chelkak, 2d ising model: Correlation functions at criticality via riemann-type boundary value problems , European Congress of Mathematics, 2018, pp. 235–256
2018
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Ron Peled and Yinon Spinka, Lectures on the spin and loop O(n) models , Springer Proceedings in Mathematics and Statistics (2019), 246–320
2019
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2020
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Dmitry Chelkak, Clément Hongler, and Konstantin Izyurov, Correlations of primary fields in the critical Ising model , 2021
2021
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Hugo Duminil-Copin, Alexander Glazman, Ron Peled, and Yinon Spinka, Macroscopic loops in the loop O ( n ) {O}(n) model at Nienhuis’ critical point , Journal of the European Mathematical Society 23
2021
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Alexander Glazman and Ioan Manolescu, Uniform Lipschitz functions on the triangular lattice have logarithmic variations , Communications in Mathematical Physics 381
2021
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Piet Lammers, Height function delocalisation on cubic planar graphs , Probab. Theory Related Fields (2021)
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Clément Hongler, Kalle Kytölä, and Fredrik Viklund, Conformal field theory at the lattice level: discrete complex analysis and virasoro structure , Communications in Mathematical Physics 395
2022
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Diederik van Engelenburg and Marcin Lis, An elementary proof of phase transition in the planar xy model , Communications in Mathematical Physics 399
2023
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2023
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by same author, Structure of Gibbs measures for planar FK-percolation and Potts models , Probability and Mathematical Physics 4
2023
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