Out-of-equilibrium critical dynamics of the three-dimensional Z_{2} gauge model along critical relaxational flows

We address the out-of-equilibrium critical dynamics of the three-dimensional lattice Z_{2} gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link Z_{2} gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice Z_{2} gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent z associated with the purely relaxational dynamics of the three-dimensional Z_{2} gauge universality class. We obtain z=2.610(15), which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.