Abstract: Assuming that the Quantum Chromodynamics (QCD) system reaches a state of thermal equilibrium, based on the universality of critical behavior, by mapping the variables of the three-dimensional Ising model onto the QCD phase plane, we investigate the density distributions of fifth-, seventh-, and ninth-order generalized susceptibilities of the net baryon number on the phase plane, as well as their dependence on the net-baryon chemical potential along the chemical freeze-out line. When only the leading-order critical contribution from the Ising model is considered, approaching the critical point from the low net-baryon chemical potential region, the generalized susceptibilities all exhibit a structure characterized by a negative dip followed by a positive peak. Upon incorporating the next-leading-order critical contribution, the presence of the negative dip becomes dependent on the distance to the phase boundary and the scaling parameters corresponding to the critical region. However, the positive peak structure remains consistently present and unaffected by these factors. In comparison to the negative dip, the positive peak structure can be considered a more robust feature indicative of the critical point.