  We determine universal critical exponents that describe the continuous phase
transitions in different dimensions of space. We use continued functions
without any external unknown parameters to obtain analytic continuation for the
recently derived 7- loop $\epsilon$ expansion from $O(n)$-symmetric $\phi^4$
field theory. Employing a new blended continued function, we obtain critical
exponent $\alpha=-0.0121(22)$ for the phase transition of superfluid helium
which matches closely with the most accurate experimental value. This result
addresses the long-standing discrepancy between the theoretical predictions and
precise experimental result of $O(2)$ $\phi^4$ model known as "$\lambda$-point
specific heat experimental anomaly". Further we have also examined the
applicability of such continued functions in other examples of field theories.
