Lattice spacing

Lattice spacing for Wilson action

This page describes the connection between the coupling parameter \(\beta\) that defines the Wilson gauge action and the lattice spacing as determined from measuring the interquark potential.

The relevant studies are:

• Nonperturbatively\[\beta\] obtained from Necco and Sommer (hep-lat/0108008, (2.6), valid up to 6.92)

• Perturbatively: perturbative \(\beta\) ((3.6) in hep-lat/9609025), matched with Necco-Sommer at 6.92

The most common formula we are going to use is the non-perturbative parametrization\[ \ln(a/r_0)=-1.6805-1.7139(\beta-6)+0.8155(\beta-6)^2- 0.6667(\beta-6)^3 \]

Since we use a heatbath algorithm together with over-relaxation steps we need to also insure that the parameters used in generating the configuration are chosen properly.

• \(n_{OR}\): this is computed using the formula from page 3 of hep-lat/9806005\[n_{OR} \approx 1.5 r_0/a\].
• \(n_{skip}\): You should also skip \(20\times (n_{OR}+1)\) steps between two measurements.