Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2004-02-19
Nucl.Phys.B699:632-656,2004
Physics
High Energy Physics
High Energy Physics - Lattice
27 pages. v2: reference and minor clarifications added, to appear in Nucl.Phys.B
Scientific paper
10.1016/j.nuclphysb.2004.08.018
Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for the scaling exponents of the gauge theory transition in the type II region, and allows thus to be scrutinized empirically. We review these predictions, and carry out numerical lattice Monte Carlo measurements to test them: a number of exponents, characterising the two phases as well as the transition point, are found to agree with expectations, supporting the conjecture. We explain why some others, like the exponent characterising the photon correlation length, appear to disagree with expectations, unless very large system sizes and the extreme vicinity of the transition point are considered. Finally, we remark that in the type I region the duality implies an interesting quantitative relationship between a magnetic flux tube and a 2-dimensional non-topological soliton.
Kajantie K.
Laine Mikko
Neuhaus Thomas
Rajantie Arttu
Rummukainen Kari
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