  Motivated by recent progress on many flavor QCD on a lattice, we investigate
conformal/walking dynamics by using Schwinger-Dyson (SD) equation within an
improved ladder approximation for two-loop running coupling. By numerically
solving the SD equation, we obtain a pole mass $m_{p}$, pion decay constant
$f_{\pi}$, and investigate the chiral symmetry breaking and mass anomalous
dimension $\gamma_{m}$ in the presence of IR cutoffs $\Lambda_{\mathrm{IR}}$.
We find that the chiral symmetry breaking is suppressed \ if IR cutoff
$\Lambda_{\mathrm{IR}}$ becomes larger than the critical \ value near the
dynamical mass ($\Lambda_{\mathrm{IR}}$ $\simeq m_{D}$) In the conformal phase
the $\gamma_{m}$ is strongly suppressed by IR cutoffs for $\Lambda
_{\mathrm{IR}}$ $\simeq m_{p}$. We, then, obtain finite size hyperscaling (FSS)
relation by adapting a linearized approximation for the SD equation, and
examine the $\gamma_{m}$ The results offer valuable insight and suggestion for
analyses in lattice gauge theories.
