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A recently proposed curvature renormalization group scheme for topologicalphase transitions defines a generic `curvature function' as a function of theparameters of the theory and shows that topological phase transitions aresignalled by the divergence of this function at certain parameters values,called critical points, in analogy with usual phase transitions. Arenormalization group procedure was also introduced as a way of flowing awayfrom the critical point towards a fixed point, where an appropriately definedcorrelation function goes to zero and topological quantum numberscharacterising the phase are easy to compute. In this paper, using twoindependent models - a model in the AIII symmetry class and a model in the BDIsymmetry class - in one dimension as examples, we show that there are caseswhere the fixed point curve and the critical point curve appear to intersect,which turn out to be multi-critical points, and focus on understanding itsimplications.

Curvature function renormalisation, topological phase transitions and multicriticality