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Nature of the antiferromagnetic quantum phase transition on the honeycomb lattice

We address the nature of the antiferromagnetic quantum phase transition that separates a semimetal from an antiferromagnet in the repulsive Hubbard model defined on the honeycomb lattice. At the critical point, the fermions acquire an anomalous dimension $η$ due to their strong coupling to the fluctuations of the order parameter $ϕ$. The finite $η$ in turn induces a singular $ϕ^{4}$ term and a non-analytical spin susceptibility signaling the breakdown of Hertz's $ϕ^{4}$ theory. As a result, the continuous antiferromagnetic quantum phase transition is internally unstable and turns into a first order transition.