Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-10-02
PoSLAT2006:042,2006
Physics
High Energy Physics
High Energy Physics - Theory
7 pages, 3 figures, talk given at Lattice 2006 (Beyond QCD)
Scientific paper
We find a strong-to-weak coupling cross-over in D=2+1 SU(N) lattice gauge theories that appears to become a third-order phase transition at N=\infty, in a similar way to the Gross-Witten transition in the D=1+1 SU(N\to\infty) lattice gauge theory. There is, in addition, a peak in the specific heat at approximately the same coupling that increases with N, which is connected to Z_N monopoles (instantons), reminiscent of the first order bulk transition that occurs in D=3+1 for N > 4. Our calculations are not precise enough to determine whether this peak is due to a second-order phase transition at N=\infty or to a third-order phase transition with different critical behaviour to that of the Gross-Witten transition. We investigate whether the trace of the Wilson loop has a non-analyticity in the coupling at some critical area, but find no evidence for this. However we do find that, just as one can prove occurs in D=1+1, the eigenvalue density of a Wilson loop forms a gap at N=\infty at a critical value of its trace. We show that this gap formation is in fact a corollary of a remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1 and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue spectra are nearly identical. This holds for finite as well as infinite N; irrespective of the Wilson loop size in lattice units; and for Polyakov as well as Wilson loops.
Bursa Francis
Teper Michael
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