Condensate of abelian monopoles and confinement in lattice gauge theories

Anatomy of the lattice magnetic monopoles

“…Indeed, the average distance between nearest monopoles in the IR cluster is about 0.5 f m, as can be extracted from the data in Refs. [3,15]. Now we observe for the first time that the excess of the action goes down when we approach the monopole center.…”

“…large enough for most of observables. On the other hand it has been found out in [3] that essentially larger volume is necessary to have only one large IR cluster. Some of our lattices are not large enough and we find on them not one but a few large clusters.…”

“…The distribution of the cluster lengths clearly shows [3] that each monopole configuration contains typically one large IR cluster and a lot of small UV clusters separated by clearly observed gap. Thus we do not need to introduce any artificial mass scale to distinguish between IR and UV clusters.…”

“…Microscopically, the condensation of the monopoles can be understood as percolation of a monopole cluster. And, indeed, it was observed that there exists always a big percolating cluster which is responsible for confinement [3]. Since the percolating cluster may seemingly have any size we will call it infrared (IR).…”

“…Since the percolating cluster may seemingly have any size we will call it infrared (IR). On the other hand, there are also many small, or ultraviolet (UV) clusters which are usually viewed as lattice artifacts [3].…”