Searching for the elusive critical endpoint at finite temperature and isospin density

We consider 3-flavour lattice QCD with a finite chemical potential mu_I for isospin, close to the finite temperature transition from hadronic matter to a quark-gluon plasma. In this region one can argue that the position and probably the nature of this transition mimic those at finite quark-number chemical potential mu. The quark mass is chosen to be close to the critical mass at zero chemical potentials. Since the Binder cumulants used to determine the nature of this transition in HMD(R) simulations are very sensitive to the updating increment dt, we have switched to the newer exact RHMC algorithm for our simulations. Preliminary results indicate that there is no critical endpoint in the small mu_I regime, at least none connected with the critical point at zero chemical potentials.