  At the point of a second order phase transition also termed as a critical
point, systems display long range order and their macroscopic behaviors are
independent of the microscopic details making up the system. Due to these
properties, it has long been speculated that biological systems that show
similar behavior despite having very different microscopics, may be operating
near a critical point. Recent methods in neuroscience are making it possible to
explore whether criticality exists in neural networks. Despite being large in
size, many data sets are still only a minute sample of the neural system and
methods towards expanding these data sets have to be considered in order to
study the existence of criticality. In this work we develop an analytical
method of expanding a dataset to the large N limit so that statements about the
critical nature of the data set could be made. We also show using a particular
dataset analyzed computationally in literature that expanding data sets keeping
the moments of the original data set need not lead to unique values of the
critical temperature when the large N limit is considered analytically, despite
the mirage of them appearing to do so when analyzed computationally. This
suggests that not all available data sets from experiments are amenable for
understanding the critically of the underlying system.
