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An introduction to lattice gauge theory and spin systems
Abstract
This article is an interdisciplinary review of lattice gauge theory and spin systems. It discusses the fundamentals, both physics and formalism, of these related subjects. Spin systems are models of magnetism and phase transitions. Lattice gauge theories are cutoff formulations of gauge theories of strongly interacting particles. Statistical mechanics and field theory are closely related subjects, and the connections between them are developed here by using the transfer matrix. Phase diagrams and critical points of continuous transitions are stressed as the keys to understanding the character and continuum limits of lattice theories. Concepts such as duality, kink condensation, and the existence of a local, relativistic field theory at a critical point of a lattice theory are illustrated in a thorough discussion of the two-dimensional Ising model. Theories with exact local (gauge) symmetries are introduced following Wegner's Ising lattice gauge theory. Its gauge-invariant "loop" correlation function is discussed in detail. Three---dimensional Ising gauge theory is studied thoroughly. The renormalization group of the two dimensional planar model is presented as an illustration of a phase transition driven by the condensation of topological excitations. Parallels are drawn to Abelian lattice gauge theory in four dimensions. Non-Abelian gauge theories are introduced and the possibility of quark confinement is discussed. Asymptotic freedom of O(n) Heisenberg spin systems in two d…
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“The lattice Hamiltonian of Eq. ( 1) can be written in the reciprocal space as”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [6]
In the citing paper
“As of now, non-Abelian lattice gauge fields have been realized experimentally using cold atoms [4,5] and electric circuits [6].”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [6]
Citations
Cites
Ordering, metastability and phase transitions in two-dimensional systems
Kosterlitz, J. M., & Thouless, D. J. (1973) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/6/7/010 · Cited by 9,639
Mermin, N. D., & Wagner, H. (1966) · Physical Review Letters · doi:10.1103/physrevlett.17.1133 · Cited by 8,363
The renormalization group and the ε expansion
Wilson, K. G. (1974) · Physics Reports · doi:10.1016/0370-1573(74)90023-4 · Cited by 5,191
Ultraviolet Behavior of Non-Abelian Gauge Theories
Gross, D. J., & Wilczek, F. A. (1973) · Physical Review Letters · doi:10.1103/physrevlett.30.1343 · Cited by 4,353
Space-Time Approach to Non-Relativistic Quantum Mechanics
Feynman, R. P. (1948) · Reviews of Modern Physics · doi:10.1103/revmodphys.20.367 · Cited by 4,239
Reliable Perturbative Results for Strong Interactions?
Politzer, H. D. (1973) · Physical Review Letters · doi:10.1103/physrevlett.30.1346 · Cited by 4,148
Introduction to Phase Transitions and Critical Phenomena
Stanley, H. E., & Wong, V. K. (1972) · American Journal of Physics · doi:10.1119/1.1986710 · Cited by 4,108
Introduction to Phase Transitions and Critical Phenomena
Stanley, E., & Ahlers, G. (1973) · Physics Today · doi:10.1063/1.3127900 · Cited by 3,690
The critical properties of the two-dimensional xy model
Kosterlitz, J. M. (1974) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/7/6/005 · Cited by 2,889
�ber das Paulische �quivalenzverbot
Jordan, P., & Wigner, E. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01331938 · Cited by 2,597
Flagged first, then by citations
Research works printed but not linked: 16
- Abers, E. S., 1973, Phys. Rev. C, 9, 1
- Baym, G., 1969, Lectures in Quantum Mechanics
- Elitzur, S., 1979, IAS preprint
- Fradkin, E., 1979, SLAC preprint
- Hamer, C. J., 1979, IAS preprint
- Kadanoff, L. P., 1976, Phase Transitions and Critical Phenomena
- Messiah, A., 1958, Quantum Mechanics
- Migdal, A. A., 1975, Zh. Eksp. Teor. Fiz., 69, 810
- Migdal, A. A., 1975, Zh. Eksp. Teor. Fiz., 69, 1457
- Polyakov, A. M., 1979, Phys. Lett. B
- Symanzik, K., 1970, Commun. Math. Phys., 49, 424
- 't Hooft, G., 1972, the Marseilles Conference on Gauge Theories
- Villain, J., 1975, J. Phys. C, 36, 581
- Wilson, K. G., 1974, Phys. Rev. D, 14, 2455
- Wortis, M., 1974, Phase Transitions and Critical Phenomena
- Yang, C. N., 1954, Phys. Rev., 96, 1605
Cited by
Sorted by citations
Items 301–400 of 1,001
Bauer, C., & Grabowska, D. M. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.l031503 · Cited by 98
Strong Pairing Originated from an Emergent Z 2 Berry Phase in La 3 Ni 2 O 7
Zhang, J., Zhang, H.-K., You, Y., & Weng, Z.-Y. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.126501 · Cited by 65
Spontaneous strong symmetry breaking in open systems: Purification perspective
Sala, P., Gopalakrishnan, S., Oshikawa, M., & You, Y. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.155150 · Cited by 93
Bulk-Boundary Correspondence for Three-Dimensional Symmetry-Protected Topological Phases
Wang, C., Lin, C.-H., & Levin, M. (2016) · Physical Review X · doi:10.1103/physrevx.6.021015 · Cited by 65
Artificial light and quantum order in systems of screened dipoles
Wen, X.-G. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.68.115413 · Cited by 74
Twist as a Probe for Phase Structure
Groeneveld, J., Jurkiewicz, J., & Altes, C. P. K. (1981) · Physica Scripta · doi:10.1088/0031-8949/23/5b/022 · Cited by 65
Bosonic many-body theory of quantum spin ice
Hao, Z., Day, A. G. R., & Gingras, M. J. P. (2014) · Physical Review B · doi:10.1103/physrevb.90.214430 · Cited by 64
Quantum simulation of ( 1 + 1 )-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases
Kuno, Y., Sakane, S., Kasamatsu, K., Ichinose, I., & Matsui, T. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.094507 · Cited by 64
Simulating Collider Physics on Quantum Computers Using Effective Field Theories
Bauer, C., Nachman, B. P., & Freytsis, M. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.212001 · Cited by 87
Self-correcting quantum memory in a thermal environment
Chesi, S., Röthlisberger, B., & Loss, D. (2010) · Physical Review A · doi:10.1103/physreva.82.022305 · Cited by 73
Goryo, J., Soma, S., & Matsukawa, H. (2007) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/80/17002 · Cited by 64
Confining QCD strings, Casimir scaling, and a Euclidean approach to high-energy scattering
Shoshi, A. I., Steffen, F. D., Dosch, H. G., & Pirner, H. J. (2003) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.68.074004 · Cited by 64
Emergent Z 2 Gauge Theories and Topological Excitations in Rydberg Atom Arrays
Samajdar, R., Joshi, D. G., Teng, Y., & Subir Sachdev, A. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.043601 · Cited by 69
Minimum instances of topological matter in an optical plaquette
Paredes, B., & Bloch, I. (2008) · Physical Review A · doi:10.1103/physreva.77.023603 · Cited by 65
High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets
Nussinov, Z., Batista, C. D., Normand, B., & Trugman, S. A. (2007) · Physical Review B · doi:10.1103/physrevb.75.094411 · Cited by 63
Dynamics of a particle in an external potential interacting with a dissipative environment
Guinea, F. (1985) · Physical review. B, Condensed matter · doi:10.1103/physrevb.32.7518 · Cited by 63
Noninvertible Symmetry-Protected Topological Order in a Group-Based Cluster State
Fechisin, C., Tantivasadakarn, N., & Albert, V. V. (2025) · Physical Review X · doi:10.1103/physrevx.15.011058 · Cited by 87
Simple Z2 lattice gauge theories at finite fermion density
Prosko, C. G., Lee, S.-P., & Maciejko, J. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.205104 · Cited by 61
Ladewig, B., Diehl, S., & Buchhold, M. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033001 · Cited by 64
Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
Choi, Y., Sanghavi, Y., Shao, S.-H., & Zheng, Y. (2025) · SciPost Physics · doi:10.21468/scipostphys.18.1.008 · Cited by 61
Analytical and non-analytical corrections to finite-size scaling
Reinicke, P. (1987) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/20/15/044 · Cited by 61
Quantum simulation of scattering in the quantum Ising model
Gustafson, E., Meurice, Y., & Unmuth-Yockey, J. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.094503 · Cited by 69
Borla, U., Verresen, R., Shah, J., & Moroz, S. (2021) · SciPost Physics · doi:10.21468/scipostphys.10.6.148 · Cited by 60
A study of d=4 U(1) lattice gauge theory with monopoles removed
Barber, J. S., Shrock, R. E., & Schrader, R. (1985) · Physics Letters B · doi:10.1016/0370-2693(85)91174-8 · Cited by 60
Novel Use of Legendre Transformation in Field Theory and Many Particle Systems
Fukuda, R., Komachiya, M., Yokojima, S., Suzuki, Y., Okumura, K., & Inagaki, T. J. (1995) · Progress of Theoretical Physics Supplement · doi:10.1143/ptps.121.1 · Cited by 60
Vortex excitations and specific heat of the planar model in two dimensions
Solla, S. A., & Riedel, E. K. (1981) · Physical review. B, Condensed matter · doi:10.1103/physrevb.23.6008 · Cited by 60
Quantum and Classical Spin-Network Algorithms for q -Deformed Kogut-Susskind Gauge Theories
Zache, T. V., González-Cuadra, D., & Zoller, P. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.171902 · Cited by 59
Visualizing dynamics of charges and strings in (2 + 1)D lattice gauge theories
Cochran, T. A., Jobst, B., Rosenberg, E. N., Lensky, Y. D., Gyawali, G., Eassa, N. M., Will, M., Szasz, A., Abanin, D. A., Acharya, R., et al. (2025) · Nature · doi:10.1038/s41586-025-08999-9 · Cited by 93
Correlated Dirac particles and superconductivity on the honeycomb lattice
Wú, W., Scherer, M. M., Carsten Honerkamp, A., & Hur, K. L. (2013) · Physical Review B · doi:10.1103/physrevb.87.094521 · Cited by 61
Exact bosonization in arbitrary dimensions
Chen, Y.-A. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033527 · Cited by 59
Higher-form symmetry breaking at Ising transitions
Zhao, J., Yan, Z., Cheng, M., & Meng, Z. Y. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.033024 · Cited by 59
Sine-Gordon theory of the non-Néel phase of two-dimensional quantum antiferromagnets
Zheng, W., & Subir Sachdev, A. (1989) · Physical review. B, Condensed matter · doi:10.1103/physrevb.40.2704 · Cited by 59
Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions
Cheng, D., Wang, K., Roques-Carmes, C., Lustig, E., Long, O. Y., Wang, H., & Fan, S. (2025) · Nature · doi:10.1038/s41586-024-08259-2 · Cited by 58
“Lattice models of gauge fields allow us to understand their physical implications in extended systems [3].”
Self-Dual Criticality in Three-Dimensional Z 2 Gauge Theory with Matter
Somoza, A. M., Serna, P., & Nahum, A. (2021) · Physical Review X · doi:10.1103/physrevx.11.041008 · Cited by 58
Illa, M., & A, M. J. S. (2022) · Physical Review A · doi:10.1103/physreva.106.052605 · Cited by 58
Single-site- and single-atom-resolved measurement of correlation functions
Endres, M., Cheneau, M., Fukuhara, T., Weitenberg, C., Schauß, P., Gross, C., Mazza, L., Bañuls, M. C., Pollet, L., Bloch, I., et al. (2013) · Applied Physics B · doi:10.1007/s00340-013-5552-9 · Cited by 64
Nonperturbative definition of the standard models
Wang, J., & Wen, X.-G. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023356 · Cited by 61
Bender, J., & Zohar, E. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.114517 · Cited by 58
Two-dimensional compact N=(2,2) lattice super-Yang–Mills theory with exact supersymmetry
Sugino, F. (2006) · Physics Letters B · doi:10.1016/j.physletb.2006.02.064 · Cited by 58
Glassy behaviour and semi-local invariance in Ising model with four-spin interaction
Lipowski, A. (1997) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/30/21/012 · Cited by 58
Theory of Hexatic-to-Hexatic Transitions
Selinger, J. V., & Nelson, D. R. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.416 · Cited by 58
Codimension-2 defects and higher symmetries in (3+1)D topological phases
Barkeshli, M., Chen, Y.-A., Huang, S.-J., Kobayashi, R., Tantivasadakarn, N., & Zhu, G. (2023) · SciPost Physics · doi:10.21468/scipostphys.14.4.065 · Cited by 57
Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large- N c Expansion
Ciavarella, A. N., & Bauer, C. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.111901 · Cited by 103
Exotic quantum phases and phase transitions in correlated matter
Alet, F., Walczak, A. M., & Fisher, M. P. A. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.04.003 · Cited by 57
The partition algebra and the Potts model transfer matrix spectrum in high dimensions
Martin, P. (2000) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/33/19/304 · Cited by 57
The pinning of a domain wall by weakened bonds in two dimensions
Chalker, J. T. (1981) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/14/9/036 · Cited by 57
Degrees and signatures of broken PT symmetry in nonuniform lattices
Scott, D. D., & Joglekar, Y. N. (2011) · Physical Review A · doi:10.1103/physreva.83.050102 · Cited by 56
Kuno, Y., Kasamatsu, K., Takahashi, Y., Ichinose, I., & Matsui, T. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/6/063005 · Cited by 56
Bonner, J. C., Blöte, H. W. J., Beck, H., & Muller, G. H. (1981) · Springer series in solid-state sciences · doi:10.1007/978-3-642-81592-8_11 · Cited by 56
Tantivasadakarn, N. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023353 · Cited by 56
Commensurate mixtures of ultracold atoms in one dimension
Mathey, L. (2007) · Physical Review B · doi:10.1103/physrevb.75.144510 · Cited by 57
Confinement and Bose condensation in gauge theory of high- Tc superconductors
Nagaosa, N., & Lee, P. A. (2000) · Physical review. B, Condensed matter · doi:10.1103/physrevb.61.9166 · Cited by 56
Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping
Kubica, A., Beverland, M. E., Brandão, F. G. S. L., Preskill, J. P., & Svore, K. M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.180501 · Cited by 55
Defect generation in a spin- 12 transverse XY chain under repeated quenching of the transverse field
Mukherjee, V., Dutta, A., & Sen, D. (2008) · Physical Review B · doi:10.1103/physrevb.77.214427 · Cited by 56
Universal properties of U(1) gauge theories
Cardy, J. (1980) · Nuclear Physics B · doi:10.1016/0550-3213(80)90417-4 · Cited by 55
Designing nonequilibrium states of quantum matter through stochastic resetting
Perfetto, G., Carollo, F., Magoni, M., & Lesanovsky, I. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.l180302 · Cited by 54
Schmidt, K. E., & Kalos, M. H. (1984) · Topics in current physics · doi:10.1007/978-3-642-96788-7_4 · Cited by 54
Identifying topological corner states in two-dimensional metal-organic frameworks
Hu, T., Zhong, W., Zhang, T., Wang, W., & Wang, Z. (2023) · Nature Communications · doi:10.1038/s41467-023-42884-1 · Cited by 58
Coarse graining of spin net models: dynamics of intertwiners
Dittrich, B., Martín-Benito, M., & Schnetter, E. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/10/103004 · Cited by 54
Interleaflet Coupling and Domain Registry in Phase-Separated Lipid Bilayers
Putzel, G., Uline, M. J., Szleifer, I. G., & Michael Schick, C. (2011) · Biophysical Journal · doi:10.1016/j.bpj.2011.01.021 · Cited by 54
Lattice model for fermionic toric code
Gu, Z., Wang, Z., & Wen, X.-G. (2014) · Physical Review B · doi:10.1103/physrevb.90.085140 · Cited by 54
Robust PT -symmetric chain and properties of its Hermitian counterpart
Joglekar, Y. N., & Saxena, A. (2011) · Physical Review A · doi:10.1103/physreva.83.050101 · Cited by 54
Scalar asymptotic charges and dual large gauge transformations
Campiglia, M., Freidel, L., Hopfmueller, F., & Soni, R. M. (2019) · Journal of High Energy Physics · doi:10.1007/jhep04(2019)003 · Cited by 54
Bovier, A., Lüling, M. G., & Wyler, D. (1981) · Journal of Mathematical Physics · doi:10.1063/1.525096 · Cited by 54
Electronic Structure Critical Parameters From Finite-Size Scaling
Neirotti, J. P., Serra, P., & Kais, S. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.3142 · Cited by 54
Mean-field theories of spin glasses
Chowdhury, D., & Mookerjee, A. (1984) · Physics Reports · doi:10.1016/0370-1573(84)90017-6 · Cited by 54
Ground state degeneracy and ferromagnetism in a spin glass
Avron, J. E., Roepstorff, G., & Schulman, L. S. (1981) · Journal of Statistical Physics · doi:10.1007/bf01106783 · Cited by 53
Symmetry-protected topological phases in lattice gauge theories: Topological QED2
Magnifico, G., Vodola, D., Ercolessi, E., Kumar, S. P., Müller, M., & Bermúdez, A. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.014503 · Cited by 53
The novel metallic states of the cuprates: Topological Fermi liquids and strange metals
Subir Sachdev, A., & Chowdhury, D. (2016) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptw110 · Cited by 53
Coarse graining flow of spin foam intertwiners
Dittrich, B., Schnetter, E., Seth, C., & Steinhaus, S. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.124050 · Cited by 57
Gauge-invariant rotor Hamiltonian from dual variables of 3D U(1) gauge theory
Unmuth-Yockey, J. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.074502 · Cited by 53
Zhou, F., & Snoek, M. (2003) · Annals of Physics · doi:10.1016/j.aop.2003.08.009 · Cited by 53
't Hooft loop in SU(2) lattice gauge theories
Tomboulis, E. T. (1981) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.23.2371 · Cited by 53
A lattice approach to spinorial quantum gravity
Renteln, P., & Smolin, L. (1989) · Classical and Quantum Gravity · doi:10.1088/0264-9381/6/3/009 · Cited by 53
Coarse graining of spin net models: dynamics of intertwinersPreprint
Dittrich, B., & Schnetter, E. (2016) · Cited by 53
Homeier, L., Bohrdt, A., Linsel, S. M., Demler, E., Halimeh, J. C., & Grusdt, F. (2023) · Communications Physics · doi:10.1038/s42005-023-01237-6 · Cited by 60
Separability Transitions in Topological States Induced by Local Decoherence
Chen, Y.-H., & Grover, T. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.170602 · Cited by 52
Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications
Pavlos, G. P., Karakatsanis, L. P., Xenakis, M. N., Pavlos, E. G., ILIOPOULOS, A. C., & Sarafopoulos, D. V. (2013) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2013.08.026 · Cited by 52
Lattice CP models and their large-N behaviour
Vecchia, P. D., Holtkamp, A., Musto, R., Nicodemi, F., & Pettorino, R. (1981) · Nuclear Physics B · doi:10.1016/0550-3213(81)90047-x · Cited by 52
Grimm, U., & Baake, M. (1997) · Springer eBooks · doi:10.1007/978-94-015-8784-6_9 · Cited by 52
Theory of symmetric electrolyte solutions: Field-theoretic approach
Kholodenko, A. L., & Beyerlein, A. L. (1986) · Physical Review A · doi:10.1103/physreva.34.3309 · Cited by 52
Vortex and fluxon phase transitions in layered superconductors
Horovitz, B. (1991) · Physical Review Letters · doi:10.1103/physrevlett.67.378 · Cited by 52
Müller, V. F., & Rühl, W. (1981) · Annals of Physics · doi:10.1016/0003-4916(81)90251-7 · Cited by 52
Buchel, A., & Pagnutti, C. (2009) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2009.08.017 · Cited by 51
Subir Sachdev, A. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(95)00657-5 · Cited by 56
Series expansions for the zero-temperature transverse Ising model
Marland, L. G. (1981) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/14/8/027 · Cited by 51
Higher-form subsystem symmetry breaking: Subdimensional criticality and fracton phase transitions
Rayhaun, B. C., & Williamson, D. J. (2023) · SciPost Physics · doi:10.21468/scipostphys.15.1.017 · Cited by 56
Observation of microscopic confinement dynamics by a tunable topological θ-angle
Zhang, W.-Y., Liu, Y., Cheng, Y., He, M.-G., Wang, H.-Y., Wang, T., Zhu, Z., Su, G.-X., Zhou, Z., Zheng, Y.-G., et al. (2024) · Nature Physics · doi:10.1038/s41567-024-02702-x · Cited by 50
Boson Pairing and Unusual Criticality in a Generalized XY Model
Shi, Y., Lamacraft, A., & Fendley, P. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.240601 · Cited by 50
The a-cycle problem for transverse Ising ring
Dong, J.-J., Li, P., & Chen, Q.-H. (2016) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2016/11/113102 · Cited by 50
Kovács, I. A., & Iglói, F. (2009) · Physical Review B · doi:10.1103/physrevb.80.214416 · Cited by 50
Abelian Higgs model: A Monte Carlo study
Callaway, D. J. E., & Carson, L. J. (1982) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.25.531 · Cited by 50
Finite renormalisations of currents in lattice gauge theories
Meyer, B., & Smith, C. N. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)90959-0 · Cited by 50
Finite-size study of the one-dimensional spin-(1/2) dimerized Heisenberg chain
Spronken, G., Fourcade, B., & Lépine, Y. (1986) · Physical review. B, Condensed matter · doi:10.1103/physrevb.33.1886 · Cited by 50
The phases of two-dimensional spin and four-dimensional gauge systems with Z(N) symmetry
Alcaraz, F. C., & Köberle, R. (1981) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/14/5/036 · Cited by 50
Application of the Green's-function Monte Carlo method to the compact Abelian lattice gauge theory
Heys, D. W., & Stump, D. R. (1983) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.28.2067 · Cited by 50
Categorical symmetries at criticality
Wu, X.-C., Ji, W., & Xu, C. (2021) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ac08fe · Cited by 49
Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches
Berghofer, P., François, J., Friederich, S., Gomes, H. D. A., Hetzroni, G., Maas, A., & Sondenheimer, R. (2023) · Cambridge University Press eBooks · doi:10.1017/9781009197236 · Cited by 60
Arbitrary dimensional Majorana dualities and architectures for topological matter
Nussinov, Z., Ortíz, G., & Cobanera, E. (2012) · Physical Review B · doi:10.1103/physrevb.86.085415 · Cited by 49
Solution to the 1+1 dimensional gauged chiral Fermion problem
Wang, J., & Wen, X.-G. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.111501 · Cited by 69
Metadata
- Authors
- Kogut, J. B.
- Affiliations
- University of Illinois Urbana-Champaign (US)
- Corresponding author
- Kogut, John B.
- ORCID
- Kogut, John B.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1979-10-01
- Volume
- 51
- Issue
- 4
- Pages
- 659-713
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W2125986857
- Cited by
- 2,029
- References
- 49
- Citations by year
- 2026: 65 · 2025: 116 · 2024: 102 · 2023: 92 · 2022: 95 · 2021: 76 · 2020: 79 · 2019: 94 · 2018: 55 · 2017: 59 · 2016: 50 · 2015: 42 · 2014: 36 · 2013: 55 · 2012: 36
- FWCI
- 39.29
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Reviews of Modern Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Keywords
- lattice gauge theory, spin systems, Ising model, transfer matrix, phase transitions, critical phenomena, duality, planar model, renormalization group, topological excitations, Abelian lattice gauge theory, Yang-Mills theory, quark confinement, asymptotic freedom
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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