  We investigate the large order aspects of the delta-expansion under the
estimation procession of the critical quantities. As illustrative examples, we
revisit one-dimensional Ising model for the analytic study and two-dimensional
square Ising model in the high temperature phase for the numerical experiment
to large orders. In both models, proposed fundamental base on which the
estimation protocol should be constructed is investigated in details and
confirmed to be valid. In the square lattice model, we present a new protocol
for the estimation of critical exponents and temperature.
