Abstract
摘要 |
We describe a numerical, Euclidean, lattice simulation of the spontaneously broken 2+1 d Abelian Higgs model in the strong coupling limit, such that the massive vector bosons and the massive neutral scalar are decoupled. This leaves a theory of light, essentially non-interacting vortices. We consider configurations of closed vortex loops, weighed by the action corresponding to the total length of vortex loops. We generate closed loops using a tetrahedral tessellation of space and set of Z_3 variables on the vertices which topologically enforce the existence of closed, non-intersecting loops. These configurations show a percolation style transition where the individual finite loops coalesce into one "infinite" loop in a bath of smaller finite loops, as the mass of the vortices becomes lighter. We compute the expectation of the Wilson loop, the Polyakov and the 'tHooft loop through the transition. In the presence of the Chern-Simons term the 'tHooft loops counts the linking number between the loops, and exhibits identical behaviour as the Wilson loop.
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