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We study the competition of spin- and charge-density waves and their quantummulticritical behavior for the semimetal-insulator transitions oflow-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawatheory with two order parameters as a model for graphene and a growing numberof other two-dimensional Dirac materials allows us to describe the physics nearthe multicritical point at which the semimetallic and the spin- andcharge-density-wave phases meet. With the help of a functional renormalizationgroup approach, we are able to reveal a complex structure of fixed points, thestability properties of which decisively depend on the number of Dirac fermions$N_f$. We give estimates for the critical exponents and observe crucialquantitative corrections as compared to the previous first-order $\epsilon$expansion. For small $N_f$, the universal behavior near the multicritical pointis determined by the chiral Heisenberg universality class supplemented by adecoupled, purely bosonic, Ising sector. At large $N_f$, a novel fixed pointwith nontrivial couplings between all sectors becomes stable. At intermediate$N_f$, including the graphene case ($N_f = 2$) no stable and physicallyadmissible fixed point exists. Graphene's phase diagram in the vicinity of theintersection between the semimetal, antiferromagnetic and staggered densityphases should consequently be governed by a triple point exhibiting first-ordertransitions.

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization