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Discrete abelian symmetries in lattice gauge theory

Discrete abelian symmetries in lattice gauge theory
Discrete abelian symmetries in lattice gauge theory

Wilson's proposed lattice approximation to Quantum Chromodynamics is reviewed, including a discussion of the approximate non-perturbative Monte Carlo method of calculation. The Transfer Matrix formulation of lattice models is discussed. This approach is used to confirm the exponential decay of the plaquette-plaquette correlation function at large distances in the Z(2) gauge model in three dimensions. Perturbative expressions are obtained for the inverse correlation length in both strong and weak coupling. 

By raising the transfer matrix to a finite power the partition function for a finite lattice Z(2) gauge model is obtained as an exact polynomial in functions of the coupling constant. The zeros of this polynomial are found and some plaquette-plaquette expectation values are extracted to test the applicability of an exponential fit for the inverse correlation length at short distances.

Similar calculations for the three dimensional Ising model are discussed in an appendix.

University of Southampton
Martin, Paul Purdon
c1b71d25-7769-42f4-9535-5899920f93b9
Martin, Paul Purdon
c1b71d25-7769-42f4-9535-5899920f93b9

Martin, Paul Purdon (1982) Discrete abelian symmetries in lattice gauge theory. University of Southampton, Doctoral Thesis, 96pp.

Record type: Thesis (Doctoral)

Abstract

Wilson's proposed lattice approximation to Quantum Chromodynamics is reviewed, including a discussion of the approximate non-perturbative Monte Carlo method of calculation. The Transfer Matrix formulation of lattice models is discussed. This approach is used to confirm the exponential decay of the plaquette-plaquette correlation function at large distances in the Z(2) gauge model in three dimensions. Perturbative expressions are obtained for the inverse correlation length in both strong and weak coupling. 

By raising the transfer matrix to a finite power the partition function for a finite lattice Z(2) gauge model is obtained as an exact polynomial in functions of the coupling constant. The zeros of this polynomial are found and some plaquette-plaquette expectation values are extracted to test the applicability of an exponential fit for the inverse correlation length at short distances.

Similar calculations for the three dimensional Ising model are discussed in an appendix.

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Published date: 1982

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Local EPrints ID: 460233
URI: http://eprints.soton.ac.uk/id/eprint/460233
PURE UUID: a5a41e08-8447-4b95-b139-e99ad6a967f3

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Date deposited: 04 Jul 2022 18:13
Last modified: 25 Oct 2023 22:53

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Author: Paul Purdon Martin

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