Do Large Abelian Monopole Loops Survive the Continuum Limit?

Details Do Large Abelian Monopole Loops Survive the Continuum Limit? Do Large Abelian Monopole Loops Survive the Continuum Limit?

1998-09-16

arxiv.org/abs/hep-lat/9809128v1

Nucl.Phys.Proc.Suppl. 73 (1999) 551-553

Physics

High Energy Physics

High Energy Physics - Lattice

LATTICE98(confine), 3 pages LaTex, uses espcrc2.sty, two eps figs

Scientific paper

10.1016/S0920-5632(99)85134-2

An analysis of the monopole loop length distribution is performed in Wilson-action SU(2) lattice gauge theory. A pure power law in the inverse length is found, at least for loops of length, $l$, less than the linear lattice size $N$. This power shows a definite $\beta$ dependence, passing 5 around $\beta =2.9$, and appears to have very little finite lattice size dependence. It is shown that when this power exceeds 5, no loops any finite fraction of the lattice size will survive the infinite lattice limit. This is true for any reasonable size distribution for loops larger than N. The apparent lack of finite size dependence in this quantity would seem to indicate that abelian monopole loops large enough to cause confinement do not survive the continuum limit. Indeed they are absent for all $\beta > 2.9$.

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