QCD with imaginary chemical potential is free of the sign problem and exhibits a rich phase structure constraining the phase diagram at real chemical potential. We simulate the critical endpoint of the Roberge-Weiss (RW) transition at imaginary chemical potential for N f " 2 QCD on Nτ " 6 lattices with standard Wilson fermions. As found on coarser lattices, the RW endpoint is a triple point connecting the deconfinement/chiral transitions in the heavy/light quark mass region and changes to a second-order endpoint for intermediate masses. These regimes are separated by two tricritical values of the quark mass, which we determine by extracting the critical exponent ν from a systematic finite size scaling analysis of the Binder cumulant of the imaginary part of the Polyakov loop. We are able to explain a previously observed finite size effect afflicting the scaling of the Binder cumulant in the regime of three-phase coexistence. Compared to Nτ " 4 lattices, the tricritical masses are significantly shifted. Exploratory results on Nτ " 8 as well as comparison with staggered simulations suggest that much finer lattices are needed before a continuum extrapolation becomes feasible.

At small lattice spacing QCD simulations are expected to become stuck in a single topological sector. Observables evaluated in a fixed topological sector differ from their counterparts in full QCD, i.e. at unfixed topology, by volume dependent corrections. We investigate these corrections in the two-flavor Schwinger model, which is in several aspects similar to QCD, using Wilson fermions. We also try to remove these corrections by suitable extrapolations to infinite volume.

For quantum field theories with topological sectors, Monte Carlo simulations on fine lattices tend to be obstructed by an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are feasible only within individual sectors. The challenge is to assemble such restricted measurements in a way that leads to a substantiated approximation to the fully fledged result, which would correspond to the correct sampling over the entire set of configurations. We test an approach for such a topological summation, which was suggested by Brower, Chandrasekharan, Negele and Wiese. Under suitable conditions, energy levels and susceptibilities can be obtained to a good accuracy, as we demonstrate for O(N) models, SU(2) Yang-Mills theory, and for the Schwinger model. 1

Abstract. We report on the status of ongoing investigations aiming at locating the deconfinement critical point with standard Wilson fermions and N f = 2 flavors towards the continuum limit (standard Columbia plot); locating the tricritical masses at imaginary chemical potential with unimproved staggered fermions at N f = 2 (extended Columbia plot); identifying the order of the chiral phase transition at µ = 0 for N f = 2 via extrapolation from non integer N f (alternative Columbia plot).