@article{MerminWagner1966,
  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},
  number = {22},
  pages = {1133--1136},
  year = {1966},
  doi = {10.1103/PhysRevLett.17.1133},
  url = {https://doi.org/10.1103/PhysRevLett.17.1133},
  note = {Erratum: Physical Review Letters 17 (1966), 1307}
}

@article{FrohlichSimonSpencer1976,
  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},
  url = {https://doi.org/10.1007/BF01608557}
}

@article{DysonLiebSimon1978,
  author = {Dyson, Freeman J. and Lieb, Elliott H. and Simon, Barry},
  title = {Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions},
  journal = {Journal of Statistical Physics},
  volume = {18},
  number = {4},
  pages = {335--383},
  year = {1978},
  doi = {10.1007/BF01106729},
  url = {https://doi.org/10.1007/BF01106729}
}

@article{Toth1993,
  author = {T{\'o}th, B{\'a}lint},
  title = {Improved Lower Bound on the Thermodynamic Pressure of the Spin {$1/2$} {Heisenberg} Ferromagnet},
  journal = {Letters in Mathematical Physics},
  volume = {28},
  number = {1},
  pages = {75--84},
  year = {1993},
  doi = {10.1007/BF00739568},
  url = {https://doi.org/10.1007/BF00739568}
}

@misc{Lieb1999,
  author = {Lieb, Elliott H.},
  title = {Long Range Order for the Quantum {Heisenberg} Model},
  howpublished = {Mathematical Physics Open Problems},
  year = {1999},
  note = {Problem A; contributed January 27, 1999.
          \href{https://web.math.princeton.edu/~aizenman/OpenProblems_MathPhys/9901.HeisenbergFerr.html}{Original problem statement}},
  url = {https://web.math.princeton.edu/~aizenman/OpenProblems_MathPhys/9901.HeisenbergFerr.html}
}

@article{NachtergaeleOgataSims2006,
  author = {Nachtergaele, Bruno and Ogata, Yoshiko and Sims, Robert},
  title = {Propagation of Correlations in Quantum Lattice Systems},
  journal = {Journal of Statistical Physics},
  volume = {124},
  pages = {1--13},
  year = {2006},
  doi = {10.1007/s10955-006-9143-6},
  eprint = {math-ph/0603064},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math-ph/0603064}
}

@article{BorceaBrandenLiggett2009,
  author = {Borcea, Julius and Br{\"a}nd{\'e}n, Petter and Liggett, Thomas M.},
  title = {Negative Dependence and the Geometry of Polynomials},
  journal = {Journal of the American Mathematical Society},
  volume = {22},
  number = {2},
  pages = {521--567},
  year = {2009},
  doi = {10.1090/S0894-0347-08-00618-8},
  eprint = {0707.2340},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0707.2340}
}

@article{CorreggiGiulianiSeiringer2015,
  author = {Correggi, Michele and Giuliani, Alessandro and Seiringer, Robert},
  title = {Validity of the Spin-Wave Approximation for the Free Energy of the {Heisenberg} Ferromagnet},
  journal = {Communications in Mathematical Physics},
  volume = {339},
  number = {1},
  pages = {279--307},
  year = {2015},
  doi = {10.1007/s00220-015-2402-0},
  eprint = {1312.7873},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1312.7873}
}

@misc{Seiringer2025,
  author = {Seiringer, Robert},
  title = {The {Heisenberg} Ferromagnet: A Dilute {Bose} Gas in Disguise},
  howpublished = {Contribution to \emph{Mini-Workshop: New Directions in Correlated Quantum Systems}, Oberwolfach Report No.~7/2025, pp.~357--358},
  year = {2025},
  doi = {10.4171/OWR/2025/7},
  url = {https://ems.press/content/serial-article-files/51350}
}


@article{Heisenberg1928,
  author = {Heisenberg, Werner},
  title = {Zur Theorie des Ferromagnetismus},
  journal = {Zeitschrift f{\"u}r Physik},
  volume = {49},
  pages = {619--636},
  year = {1928},
  doi = {10.1007/BF01328601},
  url = {https://doi.org/10.1007/BF01328601}
}

@article{Bloch1930,
  author = {Bloch, Felix},
  title = {Zur Theorie des Ferromagnetismus},
  journal = {Zeitschrift f{\"u}r Physik},
  volume = {61},
  pages = {206--219},
  year = {1930},
  doi = {10.1007/BF01339661},
  url = {https://doi.org/10.1007/BF01339661}
}

@article{Dyson1956Interactions,
  author = {Dyson, Freeman J.},
  title = {General Theory of Spin-Wave Interactions},
  journal = {Physical Review},
  volume = {102},
  number = {5},
  pages = {1217--1230},
  year = {1956},
  doi = {10.1103/PhysRev.102.1217},
  url = {https://doi.org/10.1103/PhysRev.102.1217}
}

@article{Dyson1956Thermodynamics,
  author = {Dyson, Freeman J.},
  title = {Thermodynamic Behavior of an Ideal Ferromagnet},
  journal = {Physical Review},
  volume = {102},
  number = {5},
  pages = {1230--1244},
  year = {1956},
  doi = {10.1103/PhysRev.102.1230},
  url = {https://doi.org/10.1103/PhysRev.102.1230}
}

@article{KennedyLiebShastry1988,
  author = {Kennedy, Tom and Lieb, Elliott H. and Shastry, B. Sriram},
  title = {Existence of {N{\'e}el} Order in Some Spin-{$1/2$} {Heisenberg} Antiferromagnets},
  journal = {Journal of Statistical Physics},
  volume = {53},
  number = {5--6},
  pages = {1019--1030},
  year = {1988},
  doi = {10.1007/BF01023854},
  url = {https://doi.org/10.1007/BF01023854}
}

@misc{Klippel2026FreeEnergy,
  author = {Klippel, Andreas},
  title = {Free-Energy Asymptotics of the Two-Dimensional Quantum {Heisenberg} Ferromagnet},
  year = {2026},
  eprint = {2608.25506},
  archivePrefix = {arXiv},
  primaryClass = {math-ph},
  url = {https://arxiv.org/abs/2608.25506}
}

@article{Griffiths1966,
  author = {Griffiths, Robert B.},
  title = {Spontaneous Magnetization in Idealized Ferromagnets},
  journal = {Physical Review},
  volume = {152},
  number = {1},
  pages = {240--246},
  year = {1966},
  doi = {10.1103/PhysRev.152.240}
}

@article{HaagHugenholtzWinnink1967,
  author = {Haag, Rudolf and Hugenholtz, N. M. and Winnink, Marinus},
  title = {On the equilibrium states in quantum statistical mechanics},
  journal = {Communications in Mathematical Physics},
  volume = {5},
  number = {3},
  pages = {215--236},
  year = {1967},
  doi = {10.1007/BF01646342}
}

@article{LiebRobinson1972,
  author = {Lieb, Elliott H. and Robinson, Derek W.},
  title = {The Finite Group Velocity of Quantum Spin Systems},
  journal = {Communications in Mathematical Physics},
  volume = {28},
  number = {3},
  pages = {251--257},
  year = {1972},
  doi = {10.1007/BF01645779}
}

@article{Nash1958,
  author = {Nash, John},
  title = {Continuity of Solutions of Parabolic and Elliptic Equations},
  journal = {American Journal of Mathematics},
  volume = {80}, number = {4}, pages = {931--954}, year = {1958},
  doi = {10.2307/2372841}, url = {https://doi.org/10.2307/2372841}
}
@article{DiaconisSaloffCoste1993,
  author = {Diaconis, Persi and Saloff-Coste, Laurent},
  title = {Comparison Theorems for Reversible {Markov} Chains},
  journal = {The Annals of Applied Probability},
  volume = {3}, number = {3}, pages = {696--730}, year = {1993},
  doi = {10.1214/aoap/1177005359},
  url = {https://doi.org/10.1214/aoap/1177005359}
}
@article{DiaconisSaloffCoste1996,
  author = {Diaconis, Persi and Saloff-Coste, Laurent},
  title = {{Nash} Inequalities for Finite {Markov} Chains},
  journal = {Journal of Theoretical Probability},
  volume = {9}, number = {2}, pages = {459--510}, year = {1996},
  doi = {10.1007/BF02214660}, url = {https://doi.org/10.1007/BF02214660}
}
@book{DoyleSnell1984,
  author = {Doyle, Peter G. and Snell, J. Laurie},
  title = {Random Walks and Electric Networks},
  series = {Carus Mathematical Monographs}, volume = {22},
  publisher = {Mathematical Association of America}, year = {1984},
  url = {https://arxiv.org/abs/math/0001057},
  note = {Freely available author version, arXiv:math/0001057}
}
@article{Sznitman2012,
  author = {Sznitman, Alain-Sol},
  title = {Decoupling Inequalities and Interlacement Percolation on {$G\times\mathbb Z$}},
  journal = {Inventiones Mathematicae},
  volume = {187}, number = {3}, pages = {645--706}, year = {2012},
  doi = {10.1007/s00222-011-0340-9},
  eprint = {1010.1490}, archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s00222-011-0340-9}
}
@article{Mecke1967,
  author = {Mecke, Josef},
  title = {Station{\"a}re zuf{\"a}llige Ma{\ss}e auf lokalkompakten Abelschen Gruppen},
  journal = {Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und verwandte Gebiete},
  volume = {9}, pages = {36--58}, year = {1967},
  doi = {10.1007/BF00535466}, url = {https://doi.org/10.1007/BF00535466}
}
@book{LastPenrose2017,
  author = {Last, G{\"u}nter and Penrose, Mathew},
  title = {Lectures on the {Poisson} Process},
  publisher = {Cambridge University Press}, year = {2017},
  url = {https://stoch.math.kit.edu/img/Last/lastpenrose2017.pdf}
}

@incollection{Nachtergaele1994Stochastic,
  author = {Nachtergaele, Bruno},
  title = {A Stochastic Geometric Approach to Quantum Spin Systems},
  editor = {Grimmett, Geoffrey},
  booktitle = {Probability and Phase Transition},
  series = {NATO ASI Series C},
  volume = {420},
  publisher = {Kluwer Academic Publishers},
  address = {Dordrecht},
  year = {1994},
  pages = {237--246},
  doi = {10.1007/978-94-015-8326-8_14},
  url = {https://doi.org/10.1007/978-94-015-8326-8_14}
}

@incollection{Nachtergaele1994Quasistates,
  author = {Nachtergaele, Bruno},
  title = {Quasi-state decompositions for quantum spin systems},
  booktitle = {Probability Theory and Mathematical Statistics: Proceedings of the Sixth Vilnius Conference},
  publisher = {VSP/TEV},
  address = {Utrecht--Tokyo--Vilnius},
  year = {1994},
  pages = {565--590},
  eprint = {cond-mat/9312012},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/cond-mat/9312012}
}

@article{BjornbergFrohlichUeltschi2020,
  author = {Bj{\"o}rnberg, Jakob E. and Fr{\"o}hlich, J{\"u}rg and Ueltschi, Daniel},
  title = {Quantum Spins and Random Loops on the Complete Graph},
  journal = {Communications in Mathematical Physics},
  volume = {375},
  year = {2020},
  pages = {1629--1663},
  doi = {10.1007/s00220-019-03634-x},
  eprint = {1811.12834},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s00220-019-03634-x}
}

@article{ConlonSolovej1991Representation,
  author = {Conlon, Joseph G. and Solovej, Jan Philip},
  title = {Random walk representations of the {Heisenberg} model},
  journal = {Journal of Statistical Physics},
  volume = {64},
  year = {1991},
  pages = {251--270},
  doi = {10.1007/BF01057876},
  url = {https://doi.org/10.1007/BF01057876}
}

@article{ConlonSolovej1991UpperBound,
  author = {Conlon, Joseph G. and Solovej, Jan Philip},
  title = {Upper bound on the free energy of the spin {1/2} {Heisenberg} ferromagnet},
  journal = {Letters in Mathematical Physics},
  volume = {23},
  year = {1991},
  pages = {223--231},
  doi = {10.1007/BF01885500},
  url = {https://doi.org/10.1007/BF01885500}
}

@article{MatsubaraMatsuda1956,
  author = {Matsubara, Takeo and Matsuda, Hirotsugu},
  title = {A Lattice Model of Liquid Helium, {I}},
  journal = {Progress of Theoretical Physics},
  volume = {16}, number = {6}, pages = {569--582}, year = {1956},
  doi = {10.1143/PTP.16.569},
  url = {https://doi.org/10.1143/PTP.16.569}
}

@inproceedings{DerezinskiLiangMahoney2020,
  author = {Derezi{\'n}ski, Micha{\l} and Liang, Feynman and Mahoney, Michael W.},
  title = {Exact Expressions for Double Descent and Implicit Regularization via Surrogate Random Design},
  booktitle = {Advances in Neural Information Processing Systems},
  volume = {33}, year = {2020},
  url = {https://proceedings.neurips.cc/paper_files/paper/2020/hash/37740d59bb0eb7b4493725b2e0e5289b-Abstract.html}
}

@article{AlonKozma2013LongCycles,
  author = {Alon, Gil and Kozma, Gady},
  title = {The Probability of Long Cycles in Interchange Processes},
  journal = {Duke Mathematical Journal},
  volume = {162}, number = {9}, pages = {1567--1585}, year = {2013},
  doi = {10.1215/00127094-2266018},
  eprint = {1009.3723}, archivePrefix = {arXiv},
  url = {https://doi.org/10.1215/00127094-2266018}
}

@article{Powers1976,
  author = {Powers, Robert T.},
  title = {{Heisenberg} Model and a Random Walk on the Permutation Group},
  journal = {Letters in Mathematical Physics},
  volume = {1}, number = {2}, pages = {125--130}, year = {1976},
  doi = {10.1007/BF00398374},
  url = {https://doi.org/10.1007/BF00398374}
}

@article{Timar2013,
  author = {Tim{\'a}r, {\'A}d{\'a}m},
  title = {Boundary-connectivity via graph theory},
  journal = {Proceedings of the American Mathematical Society},
  volume = {141}, number = {2}, pages = {475--480}, year = {2013},
  doi = {10.1090/S0002-9939-2012-11333-4},
  eprint = {0711.1713}, archivePrefix = {arXiv},
  url = {https://doi.org/10.1090/S0002-9939-2012-11333-4}
}

@article{Liggett2009Distributional,
  author = {Liggett, Thomas M.},
  title = {Distributional Limits for the Symmetric Exclusion Process},
  journal = {Stochastic Processes and their Applications},
  volume = {119}, number = {1}, pages = {1--15}, year = {2009},
  doi = {10.1016/j.spa.2008.01.010},
  eprint = {0710.3606}, archivePrefix = {arXiv},
  url = {https://doi.org/10.1016/j.spa.2008.01.010}
}
