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 Z(2) (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 N-f 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 N-f = 2 and within our low-order approximation, the phase diagram displays a tetracritical structure.