Roberge-Weiss transition in $N_{\text{f}}=2$ QCD with Wilson fermions and $N_{\tau }=6$

Abstract

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 $N_{\text{f}}=2$ QCD on $N_{\tau }=6$ 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 regions 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 $\nu$ 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 $N_{\tau }=4$ lattices, the tricritical masses are shifted towards smaller values. Exploratory results on $N_{\tau }=8$ as well as comparison with staggered simulations suggest that significantly finer lattices are needed before a continuum extrapolation becomes feasible.

Comments: 14 pages, 10 figures, 5 tables