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We establish a scenario where fluctuations of new degrees of freedom at aquantum phase transition change the nature of a transition beyond the standardLandau-Ginzburg paradigm. To this end we study the quantum phase transition ofgapless Dirac fermions coupled to a $\mathbb{Z}_3$ symmetric order parameterwithin a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for theKekul\'e transition in honeycomb lattice materials. For this model the standardLandau-Ginzburg approach suggests a first order transition due to thesymmetry-allowed cubic terms in the action. At zero temperature, however,quantum fluctuations of the massless Dirac fermions have to be included. Weshow that they reduce the putative first-order character of the transition andcan even render it continuous, depending on the number of Dirac fermions $N_f$.A non-perturbative functional renormalization group approach is employed toinvestigate the phase transition for a wide range of fermion numbers. For thefirst time we obtain the critical $N_f$, where the nature of the transitionchanges. Furthermore, it is shown that for large $N_f$ the change from thefirst to second order of the transition as a function of dimension occursexactly in the physical 2+1 dimensions. We compute the critical exponents andpredict sizable corrections to scaling for $N_f =2$.

Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents