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We consider some applications of the renormalization group flow equations obtained by resorting to a specific class of proper time regulators. Within this class a particular limit that corresponds to a sharpening of the effective width of the regulator is investigated and a procedure to analytically implement this limit on the flow equations is shown. We focus on the critical exponents determination for the O(N) symmetric scalar theory in three dimensions. The large N limit and some perturbative features in four dimensions are also analyzed. In all problems examined the results are optimized when the mentioned limit of the proper time regulator is taken

Proper time regulator and renormalization group flow