  We compute analytically the radiative quantum corrections, up to
next-to-leading loop order, to the universal critical exponents for both
massless and massive O($N$) $\lambda\phi^{4}$ scalar squeezed field theories
for probing the universality hypothesis. For that, we employ six distinct and
independent methods. The outcomes for the universal squeezed critical exponents
obtained through these methods are identical among them and reduce to the
conventional ones where squeezing is absent. Although the squeezing mechanism
modifies the internal properties of the field, the squeezed critical indices
are not affected by the squeezing effect, thus implying the validity of the
universality hypothesis, at least at the loop level considered. At the end, we
present the corresponding physical interpretation for the results in terms of
the geometric symmetry properties of the squeezed field.
