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Binder liked ratios of baryon number are firstly suggested in relativisticheavy ion collisions. Using 3D-Ising model, the critical behavior of Binderratios and ratios of high order cumulants of order parameter are fullypresented. Binder ratio is shown to be a step function of temperature. Thecritical point is the intersection of the ratios of different system sizesbetween two platforms. From low to high temperature through the critical point,the ratios of third order cumulants change their values from negative topositive in a valley shape, and ratios of fourth order cumulants oscillatearound zero. The normalized ratios, like the Skewness and Kurtosis, do notdiverge with correlation length, in contrary with corresponding cumulants.Applications of these characters in search critical point in relativistic heavyion collisions are discussed.

Critical behavior of Binder ratios and ratios of higher order cumulants of conserved charges in QCD deconfinement phase transition