Critical behavior of lattice models

On the self-overlap in vector spin glasses

Author(s): Hong-Bin Chen
Published in: Crossref, Issue 1, 2023
Publisher: arxiv
DOI: 10.1063/5.0196632

Near critical scaling relations for planar Bernoulli percolation without differential inequalities

Author(s): Duminil-Copin, Hugo; Manolescu, Ioan; Tassion, Vincent
Published in: Issue 6, 2021
Publisher: arxiv
DOI: 10.48550/arxiv.2111.14414

Delocalisation and continuity in 2D: loop O(2), six-vertex, and random-cluster models

Author(s): Glazman, Alexander; Lammers, Piet
Published in: 2023, Issue 3, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2306.01527

Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules

Author(s): Duminil-Copin, Hugo; Hartarsky, Ivailo
Published in: Issue 6, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2303.13920

Parisi PDE and convexity for vector spins

Author(s): Chen, Hong-Bin
Published in: Issue 3, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2311.10446

Delocalization of the height function of the six-vertex model

Author(s): Duminil-Copin, Hugo; Karrila, Alex; Manolescu, Ioan; Oulamara, Mendes
Published in: Issue 1, 2020
Publisher: arXiv

Conformal invariance of random currents: a stability result

Author(s): Chen, Hong-Bin; Xia, Jiaming
Published in: Issue 3, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2306.10625

A characterization of strong percolation via disconnection

Author(s): Duminil-Copin, Hugo; Goswami, Subhajit; Rodriguez, Pierre-François; Severo, Franco; Teixeira, Augusto
Published in: Issue 6, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2308.07920

Finite range interlacements and couplings

Author(s): Duminil-Copin, Hugo; Goswami, Subhajit; Rodriguez, Pierre-François; Severo, Franco; Teixeira, Augusto
Published in: Issue 6, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2308.07303

On Parisi measures of Potts spin glasses with correction

Author(s): Chen, Hong-Bin
Published in: Issue 3, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2311.11699

A dichotomy theory for height functions

Author(s): Lammers, Piet
Published in: Issue 2, 2022
Publisher: arxiv
DOI: 10.48550/arxiv.2211.14365

Bijecting the BKT transition

Author(s): Lammers, Piet
Published in: Issue 2, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2301.06905

Free energy in spin glass models with conventional order

Author(s): Chen, Hong-Bin
Published in: Issue 4, 2024
Publisher: arxiv
DOI: 10.48550/arxiv.2401.10223

Geometry of Gaussian free field sign clusters and random interlacements

Author(s): Drewitz, Alexander; Prévost, Alexis; Rodriguez, Pierre-François
Published in: 2018
Publisher: arXiv

Equality of critical parameters for percolation of Gaussian free field level-sets

Author(s): H. Duminil-Copin, S. Goswami, Rodriguez, Pierre-François and F. Severo
Published in: Duke Math. J., 2023, Page(s) 1-75
Publisher: arXiv
DOI: 10.1215/00127094-2022-0017

Phase transition for the vacant set of random walk and random interlacements

Author(s): Duminil-Copin, Hugo; Goswami, Subhajit; Rodriguez, Pierre-François; Severo, Franco; Teixeira, Augusto
Published in: Issue 6, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2308.07919

A PDE perspective on the Aizenman-Sims-Starr scheme

Author(s): Chen, Hong-Bin
Published in: Issue 4, 2022
Publisher: arxiv
DOI: 10.48550/arxiv.2212.09542

Conformal invariance of double random currents II: tightness and properties in the discrete

Author(s): Duminil-Copin, Hugo; Lis, Marcin; Qian, Wei
Published in: Issue 3, 2021
Publisher: arxiv
DOI: 10.48550/arxiv.2107.12880

Self-overlap correction simplifies the Parisi formula for vector spins

Author(s): Chen, Hong-Bin
Published in: Crossref, Issue 1, 2023
Publisher: arxiv
DOI: 10.1214/23-ejp1062

Long-Range Order for Critical Book-Ising and Book-Percolation

Author(s): Duminil-Copin, Hugo; Garban, Christophe; Tassion, Vincent
Published in: 2020, Issue 6, 2020
Publisher: arxiv
DOI: 10.1007/s00220-023-04856-w

On the radius of Gaussian free field excursion clusters

Author(s): Subhajit Goswami, Pierre-Francois Rodriguez, Franco Severo
Published in: 2021
Publisher: arxiv

On the free energy of vector spin glasses with non-convex interactions

Author(s): Chen, Hong-Bin; Mourrat, Jean-Christophe
Published in: https://hal.science/hal-04290374, Issue 3, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2311.08980

Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d≥3

Author(s): Hugo Duminil-Copin, Alejandro Rivera, Pierre-François Rodriguez, Hugo Vanneuville
Published in: Ann. Probab., Issue 51(1), 2023, Page(s) 228-276, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-aop1594

Emergent Planarity in two-dimensional Ising Models with finite-range Interactions

Author(s): M. Aizenman, H. Duminil-Copin, V. Tassion and S. Warzel
Published in: Inventiones Mathematicae, Issue 216, 2019, Page(s) 661–743, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-018-00851-4

Height function delocalisation on cubic planar graphs

Author(s): Piet Lammers
Published in: Probability Theory and Related Fields, Issue 182(1-2), 2022, Page(s) 531-550, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-021-01087-9

Macroscopic loops in the loop {$O(n)$} model at {N}ienhuis' critical point

Author(s): Duminil-Copin, Hugo and Glazman, Alexander and Peled, Ron and Spinka, Yinon
Published in: Journal of the European Mathematical Society, Issue 23(1), 2021, Page(s) 315-347, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1012

CLUSTER CAPACITY FUNCTIONALS AND ISOMORPHISM THEOREMSFOR GAUSSIAN FREE FIELDS

Author(s): Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
Published in: Probability theory and related fields, Issue 183(1-2), 2021, Page(s) 255-313, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-021-01090-0

Exponential decay of connection probabilities for subcritical Voronoi percolation in $\mathbb R^d$

Author(s): H. Duminil-Copin, A. Raoufi and V. Tassion
Published in: Probability Theory and Related Fields, Issue 173, 2018, Page(s) 479–490, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-018-0838-9

UST branches, martingales, and multiple SLE(2)

Author(s): Alex Karrila
Published in: Electronic Journal of Probability, Issue 25/0, 2020, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-ejp485

Universality for two-dimensional critical cellular automata

Author(s): Béla Bollobás, Hugo Duminil-Copin, Robert Morris, Paul Smith
Published in: Proceedings of the London Mathematical Society, Issue 116(2), 2023, Page(s) 620-703, ISSN 1460-244X
Publisher: Wiley
DOI: 10.1112/plms.12497

Planar random-cluster model: fractal properties of the critical phase

Author(s): Duminil-Copin, H., Manolescu, I., Tassion, V.
Published in: Probab. Theory Relat. Fields, Issue 181, 2021, Page(s) 401-449, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-021-01060-6

On the Six-Vertex Model’s Free Energy

Author(s): Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun, Ioan Manolescu & Tatiana Tikhonovskaia
Published in: Commun. Math. Phys, Issue 395, 2022, Page(s) 1383–1430, ISSN 1432-0916
Publisher: Springer verlag
DOI: 10.1007/s00220-022-04459-x

Sharp phase transition for the random-cluster and Potts models via decision trees

Author(s): H. Duminil-Copin, A. Raoufi and V. Tassion
Published in: Annals of Mathematics, Issue 189(1), 2019, Page(s) Princeton University, ISSN 0003-486X
Publisher: Princeton University Press

On the double random current nesting field

Author(s): H. Duminil-Copin and M. Lis
Published in: Probability Theory and Related Fields, Issue 175(3-4), 2019, Page(s) 937-955, ISSN 0178-8051
Publisher: Springer Verlag

Bounding the number of self-avoiding walks: Hammersley-Welsh with polygon insertion

Author(s): H. Duminil-Copin, S. Ganguly, A. Hammond, and I. Manolescu
Published in: Annals of Probability, Issue 48(4), 2020, Page(s) 1644-1692, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/19-aop1400

Existence of phase transition for percolation using the Gaussian Free Field

Author(s): H. Duminil-Copin, S. Goswami, A. Raoufi, F. Severo and A. Yadin
Published in: Duke Mathematical Journal, Issue 169(18), 2019, Page(s) 3539-3563, ISSN 0012-7094
Publisher: Duke University Press
DOI: 10.1215/00127094-2020-0036

Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature

Author(s): H. Duminil-Copin, S. Goswami and A. Raoufi
Published in: Communications in Mathematical Physics, Issue 374(2), 2020, Page(s) 891–921, ISSN 0010-3616
Publisher: Springer Verlag

Dimerization and Néel order in different quantum spin chains through a shared loop representation

Author(s): M. Aizenman, H. Duminil-Copin, and S. Warzel
Published in: Annales Henri Poincaré. A Journal of Theoretical and Mathematical Physics, Issue 21(8), 2020, Page(s) 2737--2774, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-020-00924-2

Renormalization of crossing probabilities in the planar random-cluster model

Author(s): H. Duminil-Copin and V. Tassion
Published in: Moscow Mathematical Journal, Issue 20(4), 2020, Page(s) 711--740, ISSN 1609-3321
Publisher: Independent University of Moscow
DOI: 10.17323/1609-4514-2020-20-4-711-740

Upper bounds on the percolation correlation length

Author(s): H. Duminil-Copin, G. Kozma and V. Tassion
Published in: In and out of equilibrium 3. Celebrating Vladas Sidoravicius, Issue 77, 2021, Page(s) 347-369, ISSN 1050-6977
Publisher: Birkhauser
DOI: 10.1007/978-3-030-60754-8_16

Subcritical phase of d-dimensional Poisson-Boolean percolation and its vacant set

Author(s): H. Duminil-Copin, A. Raoufi and V. Tassion
Published in: Annales Henri Lebesgue, Issue 3, 2020, Page(s) 677-700, ISSN 2644-9463
Publisher: centre mersenne
DOI: 10.5802/ahl.43

Logarithmic variance for the height function of square-ice

Author(s): H. Duminil-Copin, M. Harel, B. Laslier, A. Raoufi, G. Ray
Published in: Communications in mathematical physics, Issue 396, 2022, Page(s) 867–902, ISSN 1432-0916
Publisher: Springer
DOI: 10.1007/s00220-022-04483-x

Planar random-cluster model: scaling relations

Author(s): H.Duminil-Copin and I. Manolescu
Published in: Forum of Mathematics Pi, Issue 10, E23, 83 pages, 2023, ISSN 2050-5086
Publisher: Cambridge university press
DOI: 10.1017/fmp.2022.16

On the number of maximal paths in directed last-passage percolation

Author(s): Hugo Duminil-Copin, Harry Kesten, Fedor Nazarov, Yuval Peres, and Vladas Sidoravicius
Published in: Annals of Probability, Issue 48(5), 2020, Page(s) 2176-2188, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/19-aop1419

SIXTY YEARS OF PERCOLATION

Author(s): HUGO DUMINIL-COPIN
Published in: Proceedings of the International Congress of Mathematicians (ICM 2018), 2019, Page(s) 2829-2856, ISBN 978-981-327-288-0
Publisher: WORLD SCIENTIFIC
DOI: 10.1142/9789813272880_0162

Marginal triviality of the scaling limits of critical 4D Ising and ϕ^4_4 models

Author(s): M. Aizenman and H. Duminil-Copin
Published in: Annals of Mathematics, Issue 194(1), 2021, Page(s) 163-235, ISSN 0003-486X
Publisher: Princeton University Press
DOI: 10.4007/annals.2021.194.1.3

100 years of the (critical) Ising model on the hypercubic lattice

Author(s): Duminil-Copin, Hugo
Published in: 2022, Issue 1, 2022
Publisher: arxiv
DOI: 10.4171/icm2022/204

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