What is average plaquette?

I'm reading papers with numerical lattice results that have this quantity called 'average plaquette' but I can't find a good definition anywhere. I know what a plaquette is, the smallest loop in a lattice. But that's not a number. There's no average plaquette to be found in my books on lattice either.

My guess is this is average of energy or action of all plaquette. But I could use an actual definition.

• Sounds like a way to get through physics. – jjack Dec 24 '17 at 20:20

The smallest loop that you mention is an SU($N$) matrix (with $N=3$ for QCD). The real part of the trace of that matrix is the number in question. The average is taken over all lattice sites and orientations, so averaging over $6V$ numbers for lattice volume $V$ (in $d=4$ dimensions, where $6=d(d-1)/2$)).