@article{MW,
 author={Mermin, N. D. and Wagner, H.},
 title={Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic {Heisenberg} Models},
 journal={Physical Review Letters}, volume={17}, pages={1133--1136}, year={1966},
 doi={10.1103/PhysRevLett.17.1133}
}

@article{Mermin1967,
 author={Mermin, N. D.}, title={Absence of Ordering in Certain Classical Systems},
 journal={Journal of Mathematical Physics}, volume={8}, number={5}, pages={1061--1064}, year={1967},
 doi={10.1063/1.1705316}
}

@article{McBryanSpencer,
 author={McBryan, Oliver A. and Spencer, Thomas},
 title={On the Decay of Correlations in {SO(n)}-Symmetric Ferromagnets},
 journal={Communications in Mathematical Physics}, volume={53}, pages={299--302}, year={1977},
 doi={10.1007/BF01609854}
}

@article{GagnebinVelenik,
 author={Gagnebin, Maxime and Velenik, Yvan},
 title={Upper Bound on the Decay of Correlations in a General Class of {O(N)}-Symmetric Models},
 journal={Communications in Mathematical Physics}, volume={332}, number={3}, pages={1235--1255}, year={2014},
 doi={10.1007/s00220-014-2075-0}, eprint={1309.2432}, archivePrefix={arXiv}
}

@article{Berezinskii,
 author={Berezinskii, V. L.},
 title={Destruction of Long-Range Order in One-Dimensional and Two-Dimensional Systems Having a Continuous Symmetry Group. {I}. Classical Systems},
 journal={Soviet Physics JETP}, volume={32}, number={3}, pages={493--500}, year={1971},
 url={https://www.jetp.ras.ru/cgi-bin/dn/e_032_03_0493.pdf}
}

@article{KosterlitzThouless,
 author={Kosterlitz, J. M. and Thouless, D. J.},
 title={Ordering, Metastability and Phase Transitions in Two-Dimensional Systems},
 journal={Journal of Physics C: Solid State Physics}, volume={6}, number={7}, pages={1181--1203}, year={1973},
 doi={10.1088/0022-3719/6/7/010}
}

@article{FS,
 author={Fr{\"o}hlich, J{\"u}rg and Spencer, Thomas},
 title={The {Kosterlitz--Thouless} Transition in Two-Dimensional {Abelian} Spin Systems and the {Coulomb} Gas},
 journal={Communications in Mathematical Physics}, volume={81}, pages={527--602}, year={1981},
 doi={10.1007/BF01208273}
}

@article{AGS,
 author={Aru, Juhan and Garban, Christophe and Sep{\'u}lveda, Avelio},
 title={Percolation for {2D} Classical {Heisenberg} Model and Exit Sets of Vector Valued {GFF}},
 journal={Communications in Mathematical Physics}, volume={406}, number={2}, pages={37}, year={2025},
 doi={10.1007/s00220-024-05208-y}, eprint={2212.06767}, archivePrefix={arXiv},
 note={Article 37}
}

@article{DriesslerLandauPerez,
 author={Driessler, W. and Landau, L. and Perez, J. Fernando},
 title={Estimates of Critical Lengths and Critical Temperatures for Classical and Quantum Lattice Systems},
 journal={Journal of Statistical Physics}, volume={20}, number={2}, pages={123--162}, year={1979},
 doi={10.1007/BF01011509}
}

@article{AizenmanSimonWard,
 author={Aizenman, Michael and Simon, Barry},
 title={Local {Ward} Identities and the Decay of Correlations in Ferromagnets},
 journal={Communications in Mathematical Physics}, volume={77}, pages={137--143}, year={1980},
 doi={10.1007/BF01982713}
}

@article{Pfister,
 author={Pfister, Charles-Edouard},
 title={On the Symmetry of the {Gibbs} States in Two Dimensional Lattice Systems},
 journal={Communications in Mathematical Physics}, volume={79}, pages={181--188}, year={1981},
 doi={10.1007/BF01942060}
}

@article{Polyakov,
  author = {Polyakov, Alexander M.},
  title = {Interaction of {Goldstone} particles in two dimensions. Applications to ferromagnets and massive {Yang--Mills} fields},
  journal = {Physics Letters B}, volume = {59}, pages = {79--81}, year = {1975},
  doi = {10.1016/0370-2693(75)90161-6}
}

@article{BrezinZinnJustin,
  author = {Br{\'e}zin, {\'E}douard and Zinn-Justin, Jean},
  title = {Renormalization of the nonlinear {$\sigma$} model in {$2+\epsilon$} dimensions---Application to the {Heisenberg} ferromagnets},
  journal = {Physical Review Letters}, volume = {36}, pages = {691--694}, year = {1976},
  doi = {10.1103/PhysRevLett.36.691}
}

@article{BrezinZinnJustinSymmetry,
  author = {Br{\'e}zin, {\'E}douard and Zinn-Justin, Jean},
  title = {Spontaneous breakdown of continuous symmetries near two dimensions},
  journal = {Physical Review B}, volume = {14}, pages = {3110--3120}, year = {1976},
  doi = {10.1103/PhysRevB.14.3110}
}

@article{BrezinZinnJustinLeGuillou,
  author = {Br{\'e}zin, {\'E}douard and Zinn-Justin, Jean and Le Guillou, Jean-Claude},
  title = {Renormalization of the nonlinear {$\sigma$} model in {$2+\epsilon$} dimensions},
  journal = {Physical Review D}, volume = {14}, pages = {2615--2621}, year = {1976},
  doi = {10.1103/PhysRevD.14.2615}
}

@article{HasenfratzMaggioreNiedermayer,
  author = {Hasenfratz, Peter and Maggiore, Michele and Niedermayer, Ferenc},
  title = {The exact mass gap of the {$O(3)$} and {$O(4)$} non-linear {$\sigma$}-models in {$d=2$}},
  journal = {Physics Letters B}, volume = {245}, pages = {522--528}, year = {1990},
  doi = {10.1016/0370-2693(90)90685-Y}
}

@article{HasenfratzNiedermayer,
  author = {Hasenfratz, Peter and Niedermayer, Ferenc},
  title = {The exact mass gap of the {$O(N)$} {$\sigma$}-model for arbitrary {$N\geq3$} in {$d=2$}},
  journal = {Physics Letters B}, volume = {245}, pages = {529--532}, year = {1990},
  doi = {10.1016/0370-2693(90)90686-Z}
}

@article{HasenfratzNiedermayerPerfect1994,
  author = {Hasenfratz, Peter and Niedermayer, Ferenc},
  title = {Perfect lattice action for asymptotically free theories},
  journal = {Nuclear Physics B}, volume = {414}, pages = {785--814}, year = {1994},
  doi = {10.1016/0550-3213(94)90261-5},
  eprint = {hep-lat/9308004}, archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/hep-lat/9308004v2},
  note = {Preprint arXiv:hep-lat/9308004v2, 7 August 1993; equation locators refer to that version}
}

@article{Volin,
  author = {Volin, Dmytro},
  title = {From the mass gap at large {$N$} to the non-{Borel}-summability in {$O(3)$} and {$O(4)$} sigma models},
  journal = {Physical Review D}, volume = {81}, pages = {105008}, year = {2010},
  doi = {10.1103/PhysRevD.81.105008},
  eprint = {0904.2744}, archivePrefix = {arXiv}, primaryClass = {hep-th}
}

@article{Shin,
  author = {Shin, Dong-Shin},
  title = {Correction to four-loop {RG} functions in the two-dimensional lattice {$O(n)$} {$\sigma$}-model},
  journal = {Nuclear Physics B}, volume = {546}, pages = {669--690}, year = {1999},
  doi = {10.1016/S0550-3213(99)00020-6},
  eprint = {hep-lat/9810025}, archivePrefix = {arXiv}
}

@article{Kadanoff,
  author = {Kadanoff, Leo P.},
  title = {Scaling laws for {Ising} models near {$T_c$}},
  journal = {Physics Physique Fizika}, volume = {2}, pages = {263--272}, year = {1966},
  doi = {10.1103/PhysicsPhysiqueFizika.2.263}
}

@article{Wilson,
  author = {Wilson, Kenneth G.},
  title = {Renormalization Group and Critical Phenomena. {I}. Renormalization Group and the {Kadanoff} Scaling Picture},
  journal = {Physical Review B}, volume = {4}, pages = {3174--3183}, year = {1971},
  doi = {10.1103/PhysRevB.4.3174}
}

@article{Kupiainen,
  author = {Kupiainen, Antti J.},
  title = {On the {$1/n$} expansion},
  journal = {Communications in Mathematical Physics}, volume = {73}, pages = {273--294}, year = {1980},
  doi = {10.1007/BF01197703}
}

@article{GawedzkiKupiainen,
  author = {Gaw{\k e}dzki, Krzysztof and Kupiainen, Antti},
  title = {Continuum limit of the hierarchical {$O(N)$} non-linear {$\sigma$}-model},
  journal = {Communications in Mathematical Physics}, volume = {106}, pages = {533--550}, year = {1986},
  doi = {10.1007/BF01463394}
}

@article{MitterRamadas,
  author = {Mitter, P. K. and Ramadas, T. R.},
  title = {The two-dimensional {$O(N)$} nonlinear {$\sigma$}-model: Renormalisation and effective actions},
  journal = {Communications in Mathematical Physics}, volume = {122}, pages = {575--596}, year = {1989},
  doi = {10.1007/BF01256494}
}

@article{BalabanFlow,
  author = {Ba{\l}aban, Tadeusz},
  title = {A low temperature expansion for classical {$N$}-vector models. {I}. A renormalization group flow},
  journal = {Communications in Mathematical Physics}, volume = {167}, pages = {103--154}, year = {1995},
  doi = {10.1007/BF02099355}
}

@article{BalabanVariational,
  author = {Ba{\l}aban, Tadeusz},
  title = {The variational problems for classical {$N$}-vector models},
  journal = {Communications in Mathematical Physics}, volume = {175}, pages = {607--642}, year = {1996},
  doi = {10.1007/BF02099510}
}

@article{DybalskiStottmeisterTanimotoVariational,
  author = {Dybalski, Wojciech and Stottmeister, Alexander and Tanimoto, Yoh},
  title = {The {Ba{\l}aban} variational problem in the non-linear sigma model},
  journal = {Reviews in Mathematical Physics}, pages = {2461003}, year = {2024},
  doi = {10.1142/S0129055X24610038},
  eprint = {2403.09800}, archivePrefix = {arXiv}, primaryClass = {math-ph},
  note = {Published online 30 October 2024}
}

@article{DybalskiStottmeisterTanimotoGreen,
  author = {Dybalski, Wojciech and Stottmeister, Alexander and Tanimoto, Yoh},
  title = {Lattice {Green} functions for pedestrians: Exponential decay},
  journal = {Reviews in Mathematical Physics}, volume = {36}, number = {6}, pages = {2430005}, year = {2024},
  doi = {10.1142/S0129055X2430005X},
  eprint = {2303.10754}, archivePrefix = {arXiv}, primaryClass = {math-ph}
}

@article{Kopper,
  author = {Kopper, Christoph},
  title = {Mass generation in the large {$N$}-nonlinear {$\sigma$}-model},
  journal = {Communications in Mathematical Physics}, volume = {202}, pages = {89--126}, year = {1999},
  doi = {10.1007/s002200050576},
  eprint = {math-ph/9902020}, archivePrefix = {arXiv}
}

@article{ZamolodchikovZamolodchikov,
  author = {Zamolodchikov, Alexander B. and Zamolodchikov, Alexey B.},
  title = {Factorized {$S$}-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models},
  journal = {Annals of Physics}, volume = {120}, pages = {253--291}, year = {1979},
  doi = {10.1016/0003-4916(79)90391-9}
}

@article{PolyakovWiegmann,
  author = {Polyakov, Alexander M. and Wiegmann, P. B.},
  title = {Theory of nonabelian {Goldstone} bosons in two dimensions},
  journal = {Physics Letters B}, volume = {131}, pages = {121--126}, year = {1983},
  doi = {10.1016/0370-2693(83)91104-8}
}

@article{OS73,
  author = {Osterwalder, Konrad and Schrader, Robert},
  title = {Axioms for {Euclidean} {Green}'s functions},
  journal = {Communications in Mathematical Physics},
  volume = {31},
  number = {2},
  pages = {83--112},
  year = {1973},
  doi = {10.1007/BF01645738}
}

@article{OS75,
  author = {Osterwalder, Konrad and Schrader, Robert},
  title = {Axioms for {Euclidean} {Green}'s functions {II}},
  journal = {Communications in Mathematical Physics},
  volume = {42},
  number = {3},
  pages = {281--305},
  year = {1975},
  note = {With an Appendix by Stephen Summers},
  doi = {10.1007/BF01608978}
}

@article{FILS78,
  author = {Fr{\"o}hlich, J{\"u}rg and Israel, Robert and Lieb, Elliott H. and Simon, Barry},
  title = {Phase transitions and reflection positivity. {I}. General theory and long range lattice models},
  journal = {Communications in Mathematical Physics},
  volume = {62},
  number = {1},
  pages = {1--34},
  year = {1978},
  doi = {10.1007/BF01940327}
}

@article{FILS80,
  author = {Fr{\"o}hlich, J{\"u}rg and Israel, Robert B. and Lieb, Elliott H. and Simon, Barry},
  title = {Phase transitions and reflection positivity. {II}. Lattice systems with short-range and {Coulomb} interactions},
  journal = {Journal of Statistical Physics},
  volume = {22},
  number = {3},
  pages = {297--347},
  year = {1980},
  doi = {10.1007/BF01014646}
}

@article{OSSe78,
  author = {Osterwalder, Konrad and Seiler, Erhard},
  title = {Gauge field theories on a lattice},
  journal = {Annals of Physics},
  volume = {110},
  number = {2},
  pages = {440--471},
  year = {1978},
  doi = {10.1016/0003-4916(78)90039-8}
}

@article{FSS76,
  author = {Fr{\"o}hlich, J{\"u}rg and Simon, Barry and Spencer, Thomas},
  title = {Infrared bounds, phase transitions and continuous symmetry breaking},
  journal = {Communications in Mathematical Physics},
  volume = {50},
  number = {1},
  pages = {79--95},
  year = {1976},
  doi = {10.1007/BF01608557}
}

@article{CampbellChayes1998,
  author = {Campbell, M. and Chayes, L.},
  title = {The isotropic {O(3)} model and the {Wolff} representation},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {31}, number = {13}, pages = {L255--L259}, year = {1998},
  doi = {10.1088/0305-4470/31/13/002},
  url = {https://www.math.ucla.edu/~lchayes/lchayes_website_folder/old_publications_folder/camp_w_lett.pdf}
}

@article{FortuinKasteleynGinibre1971,
  author = {Fortuin, C. M. and Kasteleyn, P. W. and Ginibre, J.},
  title = {Correlation inequalities on some partially ordered sets},
  journal = {Communications in Mathematical Physics},
  volume = {22}, pages = {89--103}, year = {1971},
  doi = {10.1007/BF01651330}
}

@article{FortuinKasteleyn1972,
  author = {Fortuin, C. M. and Kasteleyn, P. W.},
  title = {On the random-cluster model: {I}. {Introduction} and relation to other models},
  journal = {Physica}, volume = {57}, number = {4}, pages = {536--564}, year = {1972},
  doi = {10.1016/0031-8914(72)90045-6}
}

@article{EdwardsSokal1988,
  author = {Edwards, Robert G. and Sokal, Alan D.},
  title = {Generalization of the {Fortuin--Kasteleyn--Swendsen--Wang} representation and {Monte Carlo} algorithm},
  journal = {Physical Review D}, volume = {38}, number = {6}, pages = {2009--2012}, year = {1988},
  doi = {10.1103/PhysRevD.38.2009}
}

@article{Wolff1989,
  author = {Wolff, Ulli},
  title = {Collective {Monte Carlo} updating for spin systems},
  journal = {Physical Review Letters}, volume = {62}, number = {4}, pages = {361--364}, year = {1989},
  doi = {10.1103/PhysRevLett.62.361}
}

@article{Ginibre1970,
  author = {Ginibre, J.},
  title = {General formulation of {Griffiths'} inequalities},
  journal = {Communications in Mathematical Physics}, volume = {16}, number = {4}, pages = {310--328}, year = {1970},
  doi = {10.1007/BF01646537}
}

@article{Sylvester1980,
  author = {Sylvester, Garrett S.},
  title = {The {Ginibre} inequality},
  journal = {Communications in Mathematical Physics}, volume = {73}, number = {2}, pages = {105--114}, year = {1980},
  doi = {10.1007/BF01198120}
}

@article{VanDenBergMaes1994,
  author = {van den Berg, J. and Maes, C.},
  title = {Disagreement percolation in the study of {Markov} fields},
  journal = {The Annals of Probability}, volume = {22}, number = {2}, pages = {749--763}, year = {1994},
  doi = {10.1214/aop/1176988728},
  url = {https://ir.cwi.nl/pub/1472/1472D.pdf}
}

@article{Newman1980,
  author = {Newman, Charles M.},
  title = {Normal fluctuations and the {FKG} inequalities},
  journal = {Communications in Mathematical Physics}, volume = {74}, number = {2}, pages = {119--128}, year = {1980},
  doi = {10.1007/BF01197754}
}

@article{BulinskiShabanovich1998,
  author = {Bulinski, A. V. and Shabanovich, E.},
  title = {Asymptotical behaviour for some functionals of positively and negatively dependent random fields},
  journal = {Fundamentalnaya i Prikladnaya Matematika}, volume = {4}, number = {2}, pages = {479--492}, year = {1998},
  note = {In Russian},
  url = {https://www.mathnet.ru/eng/fpm305}
}

@misc{OpenAIClassicalONDecay,
  author = {{OpenAI}},
  title = {{Exponential decay in two-dimensional classical $O(n)$ models}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026/paper.pdf}{OAI:Exponential-decay-in-two-dimensional-classical-On-models-September-23-2026}},
  year = {2026}
}
