INVESTIGATION OF A TOY MODEL FOR FRUSTRATION IN ABELIAN LATTICE GAUGE THEORY

We introduce a lattice model with local U(1) gauge symmetry which incorporates explicit frustration in d>2. The form of the action is inspired from the loop expansion of the fermionic determinant in standard lattice QED. We study through numerical simulations the phase diagram of the model, revealing the existence of a frustrated (antiferromagnetic) phase for d=3 and d=4, once an appropriate order parameter is identified.

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Phase diagram and spectrum of gauge-fixed Abelian lattice gauge theory

Physical Review D ◽

10.1103/physrevd.62.034507 ◽

2000 ◽

Vol 62 (3) ◽

Cited By ~ 11

Author(s):

Wolfgang Bock ◽

Ka Chun Leung ◽

Maarten F. L. Golterman ◽

Yigal Shamir

Keyword(s):

Phase Diagram ◽

Gauge Theory ◽

Lattice Gauge Theory ◽

Lattice Gauge ◽

Abelian Lattice

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DISCRETE GAUGE THEORIES

International Journal of Modern Physics B ◽

10.1142/s021797929100105x ◽

1991 ◽

Vol 05 (16n17) ◽

pp. 2641-2673 ◽

Cited By ~ 14

Author(s):

MARK G. ALFORD ◽

JOHN MARCH-RUSSELL

Keyword(s):

Gauge Theory ◽

Order Parameter ◽

Gauge Theories ◽

Lattice Gauge Theory ◽

Abelian Gauge ◽

Gauge Symmetries ◽

Lattice Gauge ◽

Super Conducting ◽

The Relationship ◽

Discrete Charge

In this review we discuss the formulation and distinguishing characteristics of discrete gauge theories, and describe several important applications of the concept. For the abelian (ℤN) discrete gauge theories, we consider the construction of the discrete charge operator F(Σ*) and the associated gauge-invariant order parameter that distinguishes different Higgs phases of a spontaneously broken U(1) gauge theory. We sketch some of the important thermodynamic consequences of the resultant discrete quantum hair on black holes. We further show that, as a consequence of unbroken discrete gauge symmetries, Grand Unified cosmic strings generically exhibit a Callan-Rubakov effect. For non-abelian discrete gauge theories we discuss in some detail the charge measurement process, and in the context of a lattice formulation we construct the non-abelian generalization of F(Σ*). This enables us to build the order parameter that distinguishes the different Higgs phases of a non-abelian discrete lattice gauge theory with matter. We also describe some of the fascinating phenomena associated with non-abelian gauge vortices. For example, we argue that a loop of Alice string, or any non-abelian string, is super-conducting by virtue of charged zero modes whose charge cannot be localized anywhere on or around the string (“Cheshire charge”). Finally, we discuss the relationship between discrete gauge theories and the existence of excitations possessing exotic spin and statistics (and more generally excitations whose interactions are purely “topological”).

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