Mott multicriticality of Dirac electrons in graphene

We study the multicritical behavior for the semimetal-insulator transitions on graphene's honeycomb lattice using the Gross-Neveu-Yukawa effective theory with two order parameters: the SO(3) (Heisenberg) order parameter describes the antiferromagnetic transition, and the Z2 (Ising) order parameter describes the transition to a staggered density state. Their coupling induces multicritical behavior which determines the structure of the phase diagram close to the multicritical point. Depending on the number of fermion flavors Nf and working in the perturbative regime in the vicinity of three (spatial) dimensions, we observe first-order or continuous phase transitions at the multicritical point. For the graphene case of Nf=2 and within our low-order approximation, the phase diagram displays a tetracritical structure.