  In this Letter we introduce some field-theoretic approach for computing the
critical properties of $\gamma_{KLS}$-generalized systems undergoing continuous
phase transitions, namely $\gamma_{KLS}$-statistical field theory. From this
new approach emerges the new generalized O($N$)$_{\gamma_{KLS}}$ universality
class, which is capable of encompassing nonconventional critical exponents for
real imperfect systems known as manganites not described by standard
statistical field theory. We compare the generalized results with those
obtained from measurements in manganites. The agreement was satisfactory, where
the relative errors are $< 5\%$ for the most of manganites used. Although the
present approach describes the aforementioned nonconventional critical indices,
we show that it is not complete. For example, it does not explain the results
for some other manganites, being explained only for nonextensive statistical
field theory recently introduced in literature. So, $\gamma_{KLS}$-statistical
field theory has to be discarded for statistical mechanics generalization
purposes.
