Abstract
This paper studies the vacuum overlap order parameter proposed by Fredenhagen and Marcu in the case of the compactU(1) gauge model with the Wilson action coupled to a Higgs field with fixed length |ϕ|=1. The existence of two distinct phases inD space-time dimensions (D≥4) is established.
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Fredenhagen, K., Marcu, M.: Charged states in ℤ2 gauge theories. Commun. Math. Phys.92, 81–119 (1983)
Fredenhagen, K.: Particle structure of gauge theories. Proceedings of the Summer School, “Fundamental Problems of Gauge Field Theory”, Erice 1985
Fredenhagen, K., Marcu, M.: A confinement criterium for QCD with dynamical quarks. Phys. Rev. Lett.56, 223 (1986)
Filk, T., Fredenhagen, K., Marcu, M., Slachanyi, K.: Charged states and order parameters in the Georgi-Glashow model. Desy Preprint 89-002 (1989)
Kondo, K.: Order parameter for charge confinement and phase structures in the latticeU(1) Gauge-Higgs model. Prog. Theor. Phys.74, 152–169 (1985)
Fradkin, E., Shenker, S.H.: Phase diagrams of lattice gauge theories with Higgs fields. Phys. Rev. D19, 3682 (1979)
Borgs, C., Nill, F.: The phase structure of the abelian lattice Higgs model. A review of rigorous results. J. Stat. Phys.47, 877 (1987)
King, C.: Deconfining phase transition in theU(1) model with Wilson's action. Commun. Math. Phys.105, 675–690 (1986)
Guth, A.: Existence proof of a non-confining phase in four dimensionalU(1) Lattice theory. Phys. Rev. D21, 2291–2307 (1980)
Seiler, E.: Gauge theories as a problem of constructive quantum field theory and statistical mechanics. Lecture Notes in Physics, vol. 159 Berlin, Heidelberg, New York: Springer 1982
Brydges, D.C.: A short course on cluster expansions. Les Houches lecture notes (1984)
Slachanyi, K.: Non-local fields in theZ(2) Higgs model. the global symmetry breaking and the confinement problem. Commun. Math. Phys.108, 319–352 (1987)
Ginibre, J.: General formulation of Griffths' inequalities. Commun. Math. Phys.16, 310 (1970)
Osterwalder, K., Seiler, E.: Gauge field theories on a lattice. Ann. Phys.110, 440–471 (1978)
Barata, J.C.A., Wreszinski, W.F.: Absence of charged states in theU(1) Higgs lattice Gauge theory. Commun. Math. Phys.103, 637 (1986)
Jersák, J.: Lattice Higgs models in lattice Gauge theory — a chalenge in large-scale computing. Wuppertal, 1985
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Communicated by L. Alvarez-Gaumé
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Barata, J.C.A. On the phase structure of the compact abelian lattice Higgs model. Commun.Math. Phys. 129, 511–523 (1990). https://doi.org/10.1007/BF02097103
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DOI: https://doi.org/10.1007/BF02097103