@article{athreya_convergence_1996,
	title = {On the convergence of the {Markov} chain simulation method},
	volume = {24},
	issn = {0090-5364},
	url = {https://projecteuclid.org/journals/annals-of-statistics/volume-24/issue-1/On-the-convergence-of-the-Markov-chain-simulation-method/10.1214/aos/1033066200.full},
	doi = {10.1214/aos/1033066200},
	number = {1},
	urldate = {2024-08-15},
	journal = {Ann. Stat.},
	author = {Athreya, Krishna B. and Doss, Hani and Sethuraman, Jayaram},
	month = feb,
	year = {1996},
	pages = {69-100},
}

@article{feynman_space-time_1948,
	title = {Space-{Time} {Approach} to {Non}-{Relativistic} {Quantum} {Mechanics}},
	volume = {20},
	copyright = {http://link.aps.org/licenses/aps-default-license},
	issn = {0034-6861},
	url = {https://link.aps.org/doi/10.1103/RevModPhys.20.367},
	doi = {10.1103/RevModPhys.20.367},
	language = {en},
	number = {2},
	urldate = {2024-08-15},
	journal = {Rev. Mod. Phys.},
	author = {Feynman, R. P.},
	month = apr,
	year = {1948},
	pages = {367--387},
}

@article{niedermayer_general_1988,
	title = {General {Cluster} {Updating} {Method} for {Monte} {Carlo} {Simulations}},
	volume = {61},
	copyright = {http://link.aps.org/licenses/aps-default-license},
	issn = {0031-9007},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.61.2026},
	doi = {10.1103/PhysRevLett.61.2026},
	language = {en},
	number = {18},
	urldate = {2024-08-15},
	journal = {Phys. Rev. Lett.},
	author = {Niedermayer, Ferenc},
	month = oct,
	year = {1988},
	pages = {2026--2029},
}

@article{metropolis_equation_1953,
	title = {Equation of {State} {Calculations} by {Fast} {Computing} {Machines}},
	volume = {21},
	issn = {0021-9606, 1089-7690},
	url = {https://pubs.aip.org/jcp/article/21/6/1087/202680/Equation-of-State-Calculations-by-Fast-Computing},
	doi = {10.1063/1.1699114},
	abstract = {A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two-dimensional rigid-sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four-term virial coefficient expansion.},
	language = {en},
	number = {6},
	urldate = {2024-08-15},
	journal = {J. Chem. Phys.},
	author = {Metropolis, Nicholas and Rosenbluth, Arianna W. and Rosenbluth, Marshall N. and Teller, Augusta H. and Teller, Edward},
	month = jun,
	year = {1953},
	pages = {1087--1092},
}

@article{joyce_classical_1967,
	title = {Classical {Heisenberg} {Model}},
	volume = {155},
	copyright = {http://link.aps.org/licenses/aps-default-license},
	issn = {0031-899X},
	url = {https://link.aps.org/doi/10.1103/PhysRev.155.478},
	doi = {10.1103/PhysRev.155.478},
	language = {en},
	number = {2},
	urldate = {2024-08-15},
	journal = {Phys. Rev.},
	author = {Joyce, G. S.},
	month = mar,
	year = {1967},
	pages = {478--491},
}

@article{bietenholz_topological_2010,
	title = {Topological lattice actions},
	volume = {2010},
	copyright = {http://www.springer.com/tdm},
	issn = {1029-8479},
	url = {http://link.springer.com/10.1007/JHEP12(2010)020},
	doi = {10.1007/JHEP12(2010)020},
	language = {en},
	urldate = {2024-08-15},
	journal = {J. High Energy Phys.},
	author = {Bietenholz, W. and Gerber, U. and Pepe, M. and Wiese, U.-J.},
	month = dec,
	year = {2010},
	number = {20},
}

@article{glauber_time-dependent_1963,
	title = {Time-{Dependent} {Statistics} of the {Ising} {Model}},
	volume = {4},
	issn = {0022-2488, 1089-7658},
	url = {https://pubs.aip.org/jmp/article/4/2/294/230204/Time-Dependent-Statistics-of-the-Ising-Model},
	doi = {10.1063/1.1703954},
	abstract = {The individual spins of the Ising model are assumed to interact with an external agency (e.g., a heat reservoir) which causes them to change their states randomly with time. Coupling between the spins is introduced through the assumption that the transition probabilities for any one spin depend on the values of the neighboring spins. This dependence is determined, in part, by the detailed balancing condition obeyed by the equilibrium state of the model. The Markoff process which describes the spin functions is analyzed in detail for the case of a closed N-member chain. The expectation values of the individual spins and of the products of pairs of spins, each of the pair evaluated at a different time, are found explicitly. The influence of a uniform, time-varying magnetic field upon the model is discussed, and the frequency-dependent magnetic susceptibility is found in the weak-field limit. Some fluctuation-dissipation theorems are derived which relate the susceptibility to the Fourier transform of the time-dependent correlation function of the magnetization at equilibrium.},
	language = {en},
	number = {2},
	urldate = {2024-08-15},
	journal = {J. Math. Phys.},
	author = {Glauber, Roy J.},
	month = feb,
	year = {1963},
	pages = {294--307},
}


@book{wipf_statistical_2013,
	address = {Berlin Heidelberg},
	series = {Lecture notes in physics},
	title = {Statistical approach to quantum field theory: an introduction},
	isbn = {9783642331053},
	doi = {10.1007/978-3-030-83263-6},
	shorttitle = {Statistical approach to quantum field theory},
	language = {eng},
	number = {864},
	publisher = {Springer},
	author = {Wipf, Andreas},
	year = {2013},
	pages = {7--11},
}


@article{loison_first_1998,
	title = {First and second order transition in frustrated {XY} systems},
	volume = {5},
	copyright = {http://www.springer.com/tdm},
	issn = {1434-6028},
	url = {http://link.springer.com/10.1007/s100510050497},
	doi = {10.1007/s100510050497},
	language = {en},
	number = {3},
	urldate = {2024-08-30},
	journal = {Eur. Phys. J. B},
	author = {Loison, D. and Schotte, K.D.},
	month = oct,
	year = {1998},
	pages = {735--743},
}

@article{swendsen_nonuniversal_1987,
	title = {Nonuniversal critical dynamics in {Monte} {Carlo} simulations},
	volume = {58},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.58.86},
	doi = {10.1103/PhysRevLett.58.86},
	abstract = {A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality. The algorithm violates dynamic universality at second-order phase transitions, producing unusually small values of the dynamical critical exponent.},
	number = {2},
	urldate = {2024-09-02},
	journal = {Phys. Rev. Lett.},
	author = {Swendsen, Robert H. and Wang, Jian-Sheng},
	month = jan,
	year = {1987},
	pages = {86--88},
}


@article{creutz_statistical_1981,
	title = {A statistical approach to quantum mechanics},
	volume = {132},
	copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
	issn = {00034916},
	url = {https://linkinghub.elsevier.com/retrieve/pii/0003491681900749},
	doi = {10.1016/0003-4916(81)90074-9},
	language = {en},
	number = {2},
	urldate = {2024-09-03},
	journal = {Ann. Phys.},
	author = {Creutz, M and Freedman, B},
	month = apr,
	year = {1981},
	pages = {427--462},
}


@article{giachetti_berezinskii-kosterlitz-thouless_2021,
	title = {Berezinskii-{Kosterlitz}-{Thouless} {Phase} {Transitions} with {Long}-{Range} {Couplings}},
	volume = {127},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.127.156801},
	doi = {10.1103/PhysRevLett.127.156801},
	language = {en},
	number = {15},
	urldate = {2024-09-03},
	journal = {Phys. Rev. Lett.},
	author = {Giachetti, Guido and Defenu, Nicolò and Ruffo, Stefano and Trombettoni, Andrea},
	month = oct,
	year = {2021},
	pages = {156801},
}


@book{yeomans_statistical_1992,
	address = {Oxford [England] : New York},
	series = {Oxford science publications},
	title = {Statistical mechanics of phase transitions},
	isbn = {9780198517306 9780198517290},
	publisher = {Oxford University Press},
	author = {Yeomans, J. M.},
	year = {1992},
	keywords = {Phase transformations (Statistical physics)},
	pages = {16--19},
	url = "https://isbnsearch.org/isbn/9780198517306"
}

@article{kosterlitz_long_1972,
	title = {Long range order and metastability in two dimensional solids and superfluids. ({Application} of dislocation theory)},
	volume = {5},
	issn = {0022-3719},
	url = {https://iopscience.iop.org/article/10.1088/0022-3719/5/11/002},
	doi = {10.1088/0022-3719/5/11/002},
	number = {11},
	urldate = {2024-09-06},
	journal = {	J. Phys. Condens. Matter},
	author = {Kosterlitz, J M and Thouless, D J},
	month = jun,
	year = {1972},
	pages = {124--126},
}

@article{kosterlitz_nobel_2017,
	title = {Nobel {Lecture}: {Topological} defects and phase transitions},
	volume = {89},
	copyright = {https://link.aps.org/licenses/aps-default-license},
	issn = {0034-6861, 1539-0756},
	shorttitle = {Nobel {Lecture}},
	url = {https://link.aps.org/doi/10.1103/RevModPhys.89.040501},
	doi = {10.1103/RevModPhys.89.040501},
	language = {en},
	number = {4},
	urldate = {2024-09-06},
	journal = {Rev. Mod. Phys.},
	author = {Kosterlitz, John Michael},
	month = oct,
	year = {2017},
}


@article{van_oosterom_solid_1983,
	title = {The {Solid} {Angle} of a {Plane} {Triangle}},
	volume = {BME-30},
	copyright = {https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html},
	issn = {0018-9294},
	url = {http://ieeexplore.ieee.org/document/4121581/},
	doi = {10.1109/TBME.1983.325207},
	number = {2},
	urldate = {2024-10-29},
	journal = {IEEE Transactions on Biomedical Engineering},
	author = {Van Oosterom, A. and Strackee, J.},
	month = feb,
	year = {1983},
	pages = {125--126},
}


@article{berg_definition_1981,
	title = {Definition and statistical distributions of a topological number in the lattice {O}(3) σ-model},
	volume = {190},
	copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
	issn = {05503213},
	url = {https://linkinghub.elsevier.com/retrieve/pii/055032138190568X},
	doi = {10.1016/0550-3213(81)90568-X},
	language = {en},
	number = {2},
	urldate = {2025-02-12},
	journal = {Nucl. Phys.},
	author = {Berg, B. and Lüscher, M.},
	month = aug,
	year = {1981},
	pages = {412--424},
}

@article{eriksson_measure_1990,
	title = {On the {Measure} of {Solid} {Angles}},
	volume = {63},
	issn = {0025-570X, 1930-0980},
	url = {https://www.tandfonline.com/doi/full/10.1080/0025570X.1990.11977515},
	doi = {10.1080/0025570X.1990.11977515},
	language = {en},
	number = {3},
	urldate = {2025-02-14},
	journal = {Math. Mag.},
	author = {Eriksson, Folke},
	month = jun,
	year = {1990},
	pages = {184--187},
}

@article{kibble_phase-transition_2007,
	title = {Phase-transition dynamics in the lab and the universe},
	volume = {60},
	issn = {0031-9228, 1945-0699},
	url = {https://pubs.aip.org/physicstoday/article/60/9/47/395625/Phase-transition-dynamics-in-the-lab-and-the},
	doi = {10.1063/1.2784684},
	abstract = {Topological defects, such as vortices and flux tubes, that arise during phase transitions in condensed-matter systems can serve as models for a far more elusive defect—cosmic strings formed in the early universe.},
	language = {en},
	number = {9},
	urldate = {2025-02-21},
	journal = {Phys. Today},
	author = {Kibble, Tom},
	month = sep,
	year = {2007},
	pages = {47--52},
}

@article{kibble_topology_1976,
	title = {Topology of cosmic domains and strings},
	volume = {9},
	issn = {0305-4470, 1361-6447},
	url = {https://iopscience.iop.org/article/10.1088/0305-4470/9/8/029},
	doi = {10.1088/0305-4470/9/8/029},
	number = {8},
	urldate = {2025-03-07},
	journal = {J. Phys. A},
	author = {Kibble, T W B},
	month = aug,
	year = {1976},
	pages = {1387--1398},
}

@article{kibble_implications_1980,
	title = {Some implications of a cosmological phase transition},
	volume = {67},
	copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
	issn = {03701573},
	url = {https://linkinghub.elsevier.com/retrieve/pii/0370157380900915},
	doi = {10.1016/0370-1573(80)90091-5},
	language = {en},
	number = {1},
	urldate = {2025-03-07},
	journal = {Phys. Rep.},
	author = {Kibble, T.W.B.},
	month = dec,
	year = {1980},
	pages = {183--199},
}

@article{zurek_cosmological_1985,
	title = {Cosmological experiments in superfluid helium?},
	volume = {317},
	copyright = {http://www.springer.com/tdm},
	issn = {0028-0836, 1476-4687},
	url = {https://www.nature.com/articles/317505a0},
	doi = {10.1038/317505a0},
	language = {en},
	number = {6037},
	urldate = {2025-03-07},
	journal = {Nat.},
	author = {Zurek, W. H.},
	month = oct,
	year = {1985},
	pages = {505--508},
}

@article{wolff_collective_1989,
	title = {Collective {Monte} {Carlo} {Updating} for {Spin} {Systems}},
	volume = {62},
	copyright = {http://link.aps.org/licenses/aps-default-license},
	issn = {0031-9007},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.62.361},
	doi = {10.1103/PhysRevLett.62.361},
	language = {en},
	number = {4},
	urldate = {2025-03-07},
	journal = {Phys. Rev. Lett.},
	author = {Wolff, Ulli},
	month = jan,
	year = {1989},
	pages = {361--364},
}


@article{ciuca_information_2020,
	title = {Information theoretic bounds on cosmic string detection in {CMB} maps with noise},
	volume = {492},
	copyright = {https://academic.oup.com/journals/pages/open\_access/funder\_policies/chorus/standard\_publication\_model},
	issn = {0035-8711, 1365-2966},
	url = {https://academic.oup.com/mnras/article/492/1/1329/5680503},
	doi = {10.1093/mnras/stz3551},
	abstract = {ABSTRACT
            We use a convolutional neural network to study cosmic string detection in cosmic microwave background (CMB) flat sky maps with Nambu–Goto strings. On noiseless maps, we can measure string tensions down to order 10−9, however when noise is included we are unable to measure string tensions below 10−7. Motivated by this impasse, we derive an information theoretic bound on the detection of the cosmic string tension Gμ from CMB maps. In particular, we bound the information entropy of the posterior distribution of Gμ in terms of the resolution, noise level and total survey area of the CMB map. We evaluate these bounds for the ACT, SPT-3G, Simons Observatory, Cosmic Origins Explorer, and CMB-S4 experiments. These bounds cannot be saturated by any method.},
	language = {en},
	number = {1},
	urldate = {2025-03-07},
	journal = {Mon. Not. R. Astron. Soc.},
	author = {Ciuca, Razvan and Hernández, Oscar F},
	month = feb,
	year = {2020},
	pages = {1329--1334},
}

@book{binder_monte_1988,
	address = {Berlin, Heidelberg},
	series = {Springer {Series} in {Solid}-{State} {Sciences}},
	title = {Monte {Carlo} {Simulation} in {Statistical} {Physics}},
	volume = {80},
	copyright = {http://www.springer.com/tdm},
	isbn = {9783662088562 9783662088548},
	url = {http://link.springer.com/10.1007/978-3-662-08854-8},
	urldate = {2025-03-07},
	publisher = {Springer},
	author = {Binder, Kurt and Heermann, Dieter W.},
	editor = {Cardona, Manuel and Fulde, Peter and Von Klitzing, Klaus and Queisser, Hans-Joachim and Lotsch, Helmut K. V.},
	year = {1988},
	doi = {10.1007/978-3-662-08854-8},
}

@book{schulman_techniques_2005,
	address = {Mineola, N.Y},
	edition = {Expanded republ. of the 1996 print},
	title = {Techniques and applications of path integration},
	isbn = {9780486445281},
	language = {eng},
	publisher = {Dover Publications},
	author = {Schulman, Lawrence S. and Schulman, Lawrence S.},
	year = {2005},
}

@article{wilson_renormalization_1974,
	title = {The renormalization group and the ε expansion},
	volume = {12},
	copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
	issn = {03701573},
	url = {https://linkinghub.elsevier.com/retrieve/pii/0370157374900234},
	doi = {10.1016/0370-1573(74)90023-4},
	number = {2},
	urldate = {2025-03-07},
	journal = {Phys. Rep.},
	author = {Wilson, K},
	month = aug,
	year = {1974},
	pages = {75--199},
}

@article{hinrichsen_non-equilibrium_2000,
	title = {Non-equilibrium critical phenomena and phase transitions into absorbing states},
	volume = {49},
	issn = {0001-8732, 1460-6976},
	url = {http://www.tandfonline.com/doi/abs/10.1080/00018730050198152},
	doi = {10.1080/00018730050198152},
	language = {en},
	number = {7},
	urldate = {2025-03-07},
	journal = {Adv. Phys.},
	author = {Hinrichsen, Haye},
	month = nov,
	year = {2000},
	pages = {815--958},
}

@book{todhunter_spherical_2021,
	address = {[S.l.]},
	title = {Spherical Trigonometry},
	isbn = {9788180940521},
	language = {eng},
	publisher = {Macmillan And Company},
	author = {Todhunter, I.},
	year = {1925},
	note = {OCLC: 1273678656},
	pages = {20--44},
	url = "https://archive.org/details/in.ernet.dli.2015.216425"
}


@article{hoshen_percolation_1976,
	title = {Percolation and cluster distribution. {I}. {Cluster} multiple labeling technique and critical concentration algorithm},
	volume = {14},
	copyright = {http://link.aps.org/licenses/aps-default-license},
	issn = {0556-2805},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.14.3438},
	doi = {10.1103/PhysRevB.14.3438},
	language = {en},
	number = {8},
	urldate = {2025-03-28},
	journal = {Phys. Rev. B},
	author = {Hoshen, J. and Kopelman, R.},
	month = oct,
	year = {1976},
	pages = {3438--3445},
}


@article{lin_topological_2014,
	title = {Topological defects as relics of emergent continuous symmetry and {Higgs} condensation of disorder in ferroelectrics},
	volume = {10},
	issn = {1745-2473, 1745-2481},
	url = {https://www.nature.com/articles/nphys3142},
	doi = {10.1038/nphys3142},
	language = {en},
	number = {12},
	urldate = {2025-06-05},
	journal = {Nat. Phys.},
	author = {Lin, Shi-Zeng and Wang, Xueyun and Kamiya, Yoshitomo and Chern, Gia-Wei and Fan, Fei and Fan, David and Casas, Brian and Liu, Yue and Kiryukhin, Valery and Zurek, Wojciech H. and Batista, Cristian D. and Cheong, Sang-Wook},
	month = dec,
	year = {2014},
	pages = {970--977},
}

@article{zeng_universal_2023,
	title = {Universal {Breakdown} of {Kibble}-{Zurek} {Scaling} in {Fast} {Quenches} across a {Phase} {Transition}},
	volume = {130},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.130.060402},
	doi = {10.1103/PhysRevLett.130.060402},
	language = {en},
	number = {6},
	urldate = {2025-07-02},
	journal = {Phys. Rev. Lett.},
	author = {Zeng, Hua-Bi and Xia, Chuan-Yin and Del Campo, Adolfo},
	month = feb,
	year = {2023},
	pages = {060402},
}

@article{bietenholz_topological_2018,
	title = {Topological susceptibility of the {2D} {O}(3) model under gradient flow},
	volume = {98},
	issn = {2470-0010, 2470-0029},
	url = {https://link.aps.org/doi/10.1103/PhysRevD.98.114501},
	doi = {10.1103/PhysRevD.98.114501},
	language = {en},
	number = {11},
	urldate = {2025-07-02},
	journal = {Phys. Rev.},
	author = {Bietenholz, Wolfgang and De Forcrand, Philippe and Gerber, Urs and Mejía-Díaz, Héctor and Sandoval, Ilya O.},
	month = dec,
	year = {2018},
	pages = {114501},
}

@article{eriksson_measure_1990,
	title = {On the {Measure} of {Solid} {Angles}},
	volume = {63},
	issn = {0025-570X, 1930-0980},
	url = {https://www.tandfonline.com/doi/full/10.1080/0025570X.1990.11977515},
	doi = {10.1080/0025570X.1990.11977515},
	language = {en},
	number = {3},
	urldate = {2025-08-06},
	journal = {Math. Mag.},
	author = {Eriksson, Folke},
	month = jun,
	year = {1990},
	pages = {184--187},
}

@article{kadanoff_scaling_1966,
	title = {Scaling laws for ising models near {T} c},
	volume = {2},
	copyright = {https://link.aps.org/licenses/aps-default-license},
	issn = {0554-128X},
	url = {https://link.aps.org/doi/10.1103/PhysicsPhysiqueFizika.2.263},
	doi = {10.1103/PhysicsPhysiqueFizika.2.263},
	language = {en},
	number = {6},
	urldate = {2025-08-20},
	journal = {Phys. Phys. Fiz.},
	author = {Kadanoff, Leo P.},
	month = jun,
	year = {1966},
	pages = {263--272},
}

@article{kadanoff_static_1967,
	title = {Static {Phenomena} {Near} {Critical} {Points}: {Theory} and {Experiment}},
	volume = {39},
	copyright = {http://link.aps.org/licenses/aps-default-license},
	issn = {0034-6861},
	shorttitle = {Static {Phenomena} {Near} {Critical} {Points}},
	url = {https://link.aps.org/doi/10.1103/RevModPhys.39.395},
	doi = {10.1103/RevModPhys.39.395},
	language = {en},
	number = {2},
	urldate = {2025-08-20},
	journal = {Rev. Mod. Phys},
	author = {Kadanoff, Leo P. and Götze, Wolfgang and Hamblen, David and Hecht, Robert and Lewis, E. A. S. and Palciauskas, V. V. and Rayl, Martin and Swift, J. and Aspnes, David and Kane, Joseph},
	month = apr,
	year = {1967},
	pages = {395--431},
}

@article{trotter_product_1959,
	title = {On the product of semi-groups of operators},
	volume = {10},
	issn = {0002-9939, 1088-6826},
	url = {https://www.ams.org/proc/1959-010-04/S0002-9939-1959-0108732-6/},
	doi = {10.1090/S0002-9939-1959-0108732-6},
	language = {en},
	number = {4},
	urldate = {2025-08-30},
	journal = {Proceedings of the American Mathematical Society},
	author = {Trotter, H. F.},
	month = aug,
	year = {1959},
	pages = {545--551},
}