A measure of data collapse for scaling

Abstract

Data collapse is a way of establishing scaling and extracting associated exponents in problems showing self-similar or self-affine characteristics as, for example, in equilibrium or non-equilibrium phase transitions, in critical phases, in dynamics of complex systems and many others. We propose a measure to quantify the nature of data collapse. Via a minimization of this measure, the exponents and their error-bars can be obtained. The procedure is illustrated by considering finite-size-scaling near phase transitions and quite strikingly recovering the exact exponents.