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For small volume of the quark-gluon plasma formed in heavy ion collisions,the observable near criticality must obey finite-size scaling. According to thefinite-size scaling, there exists a fixed point at the critical temperature,where scaled susceptibility at different system sizes intersect. It also existsat the transitional temperature of a first order phase transition and can begeneralized to the region of the crossover. In order to quantify the feature ofthe fixed point, we introduce {\it the width of a set of points}. When allpoints in the set are in their mean position within error, the width reachesits minimum, and all points merge into the fixed point. Using the observableproduced by the Potts model, we demonstrate that the contour plot of the widthdefined in this study clearly indicates the temperatures and exponent ratios offixed point, which could correspond to either the critical point, the points onthe transition line, or the crossover region. This method is thereforeinstructive to the determination of QCD phase boundary by beam energy scan inrelativistic heavy ion collisions.

How to locate the QCD phase boundary by scanning observable in the phase plane