Nucleation-type criticality with infinite number of free-energy minima beyond mean-field theory

We study the phase diagram of a three-dimensional Heisenberg model with Dzyaloshinski--Moriya interaction under the presence of Potts-like anisotropy. The phase transition between the winding phase and the ferromagnetically ordered phase exhibits a critical phase transition with anomalous features such as critical exponents consistent with that of a first-order transition while maintaining continuity of physical quantities. Furthermore, at the critical point, we see a growing number of free energy local minima, supporting the picture of infinitely many discontinuous transitions forming criticality. Our numerical result unify de Gennes' theory of nucleation-type transitions and Dzyaloshinskii's calculation of chiral magnets by demonstrating that such anomalous criticality can be realized in microscopic models beyond mean-field.