Measuring the derivatives of couplings with respect to lattice spacing for dynamical Wilson fermions

In finite temperature QCD, the calculation of thermodynamic quantities requires the derivatives of the couplings with respect to lattice spacings in different directions. A method of calculating these derivatives from measurements of long distance observables on a set of three lattices with symmetric and asymmetric couplings is presented. Our simulations at β = 5.3 and κ = 0.158 indicate that an asymmetric change in the gauge couplings does not produce an asymmetric lattice, within statistical errors, while changing κ asymmetrically does produce different lattice spacings. This indicates that the derivatives of the gauge couplings with respect to different lattice spacings are large and their perturbative values should not be used in the calculation of nonperturbative thermodynamic quantities.