The multi-critical fixed points of O(N) symmetric models cease to exist in the N→∞ limit, but the mechanism regulating their annihilation still presents several enigmatic aspects. Here, we explore the evolution of high-order multi-critical points in the (d,N) plane and uncover a complex mosaics for their asymptotic behaviour at large N. This picture is confirmed by various RG approaches and constitutes a fundamental step towards the full comprehension of critical behaviour in O(N) field theories.


Related to Project: C02, C03