  A popular measure for citation inequalities of individual scientists has been
the Hirsch index ($h$). If for any scientist the number $n_c$ of citations is
plotted against the serial number $n_p$ of the paper having those many
citations (when the papers are ordered from highest cited to lowest) then $h$
corresponds to the nearest lower integer value of $n_p$ below the fixed point
of the non-linear citation function (or given by $n_c = h = n_p$ if both $n_p$
and $n_c$ are dense set of integers near the $h$ value). The same index can be
estimated (from $h=s=n_{s}$) for the avalanche or cluster of size ($s$)
distributions ($n_s$) in elastic fiber bundle or percolation models. Another
such inequality index, called the Kolkata index ($k$) says that $(1-k)$
fraction of papers attract $k$ fraction of citations ($k=0.80$ corresponds to
the 80-20 law of Pareto). We find, for stress ($\sigma$), lattice occupation
probability ($p$) or Kolkata index ($k$) near the bundle failure threshold
($\sigma_c$) or percolation threshold ($p_c$) or critical value of Kolkata
index $k_c$, good fit to Widom-Stauffer like scaling $h/[\sqrt{N}/log N]$ =
$f(\sqrt{N}[\sigma_c -\sigma]^\alpha)$, $h/[\sqrt{N}/log N]=f(\sqrt{N}|p_c
-p|^\alpha)$ or $h/[\sqrt{N_c}/log N_c]=f(\sqrt{N_c}|k_c -k|^\alpha)$
respectively, with asymptotically defined scaling function $f$, for systems of
size $N$ (total number of fibers or lattice sites) or $N_c$ (total number of
citations), and $\alpha$ denoting the appropriate scaling exponent. We also
show that if the number ($N_m$) of members of parliaments or national
assemblies of different countries (with population $N$) is identified as their
respective $h-$index, then the data fit the scaling relation $N_m \sim \sqrt N
/log N$, resolving a major recent controversy.
