  A recently proposed curvature renormalization group scheme for topological
phase transitions defines a generic `curvature function' as a function of the
parameters of the theory and shows that topological phase transitions are
signalled by the divergence of this function at certain parameters values,
called critical points, in analogy with usual phase transitions. A
renormalization group procedure was also introduced as a way of flowing away
from the critical point towards a fixed point, where an appropriately defined
correlation function goes to zero and topological quantum numbers
characterising the phase are easy to compute. In this paper, using two
independent models - a model in the AIII symmetry class and a model in the BDI
symmetry class - in one dimension as examples, we show that there are cases
where the fixed point curve and the critical point curve appear to intersect,
which turn out to be multi-critical points, and focus on understanding its
implications.
