  The Efimov effect is the only experimentally realized universal phenomenon
that exhibits the renormalization-group limit cycle with the three-body
parameter parametrizing a family of universality classes. Recent experiments in
ultracold atoms have unexpectedly revealed that the three-body parameter itself
is universal when measured in units of an effective range. By performing an
exact functional renormalization-group analysis with various finite-range
interaction potentials, we demonstrate that the onset of the
renormalization-group flow into the limit cycle is universal, regardless of
short-range details, which connects the missing link between the two
universalities of the Efimov physics. A close connection between the
topological property of the limit cycle and few-body physics is also
delineated.
