Geometrical aspect of susceptibility critical exponent

Critical exponent $gamma succeq 1.1$ characterizes behavior of the mechanical susceptibility of a real fluid when temperature approaches the critical one. It definitely results in the zero Gaussian curvature of the local shape of the critical point on the thermodynamic equation of state surface, which imposes a new constraint upon the construction of the potential equation of state of the real fluid from the empirical data. All known empirical equations of state suffer from a weakness that the Gaussian curvature of the critical point is negative definite instead of zero, and a new equations of state for the vapor-liquid phase transition with $gamma succ 1$ is constructed.