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Cited by 2,029Theoretical and Computational PhysicsQuantum Chromodynamics and Particle InteractionsParticle physics theoretical and experimental studies

An introduction to lattice gauge theory and spin systems

Kogut, John B.·1979·Reviews of Modern Physics
DOI 10.1103/revmodphys.51.659
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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 reciprocal space as Eq. (2), which is a Yang-Mills Hamiltonian.

    “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]

  • Non-Abelian lattice gauge fields have been realized experimentally using cold atoms and electric circuits.

    “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]

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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)
DOI
10.1103/revmodphys.51.659
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
Licence
link.aps.org/licenses/aps-default-license (vor)
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

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