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 ${\mathbb{Z}}_2$ (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.

• Received 31 March 2015

DOI:https://doi.org/10.1103/PhysRevB.92.035429

Source: http://link.aps.org/doi/10.1103/PhysRevB.92.035429