Numerical study of the equation of state for two flavor QCD at finite density

We discuss the equation of state for 2 flavor QCD at non-zero temperature anddensity. Derivatives of $\ln Z$ with respect to quark chemical potential$\mu_q$ up to fourth order are calculated, enabling estimates of the pressure,quark number density and associated susceptibilities as functions of $\mu_q$via a Taylor series expansion. It is found that the fluctuations in the quarknumber density increase in the vicinity of the phase transition temperature andthe susceptibilities start to develop a pronounced peak as $\mu_q$ isincreased. This suggests the presence of a critical endpoint in the $(T,\mu_q)$ plane.