Progress on the QCD deconfinement critical point for $N_{\text{f}}=2$ staggered fermions

The global center symmetry of quenched QCD at zero baryonic chemical potential is broken spontaneously at a critical temperature $T_c$ leading to a first-order phase transition. Including heavy dynamical quarks breaks the center symmetry explicitly and weakens the first-order phase transition for decreasing quark masses until it turns into a smooth crossover at a $Z(2)$-critical point. We investigate the $Z(2)$-critical quark mass value towards the continuum limit for $N_{\text{f}}=2$ flavors using lattice QCD in the staggered formulation. As part of a continued study, we present results from Monte-Carlo simulations on $N_{\tau }=8,10$ lattices. Several aspect ratios and quark mass values were simulated in order to obtain the critical mass from a fit of the Polyakov loop to a kurtosis finite size scaling formula. Moreover, the possibility to develop a Ginzburg-Landau effective theory around the $Z(2)$-critical point is explored.