  We use the linear sigma model with quarks to locate the critical end point in
the effective QCD phase diagram accounting for fluctuations in temperature and
quark chemical potential. For this purpose, we use the non-equilibrium
formalism provided by the superstatistics framework. We compute the effective
potential in the high- and low-temperature approximations up to sixth order and
include the contribution of ring diagrams to account for plasma screening
effects. We fix the model parameters from relations between the thermal sigma
and pion masses imposing a first order phase transition at zero temperature and
a finite critical value for the baryon chemical potential that we take of order
of the nucleon mass. We find that the CEP displacement due to fluctuations in
temperature and/or quark chemical potential is almost negligible.
