  We study the effect of presence of different types of critical points such as
ordinary critical point, multicritical point and quasicritical point along
different paths on the Fidelity susceptibility and Loschmidt echo of a three
spin interacting transverse Ising chain using a method which does not involve
the language of tensors. We find that the scaling of fidelity susceptibility
and Loschmidt echo with the system size at these special critical points of the
model studied, is in agreement with the known results, thus supporting our
method.
