irrelevant (in the Weyl semimetal), justifying our treatment of the phase diagram to a first approximation.

More subtle effects may make small modifications to this picture. Coulomb interactions can destabilize some of the quantum phase transitions in Figure \[fig1\], leading to intermediate phases. When the magnetic field is applied along a low symmetry axis, the double Weyl points can split into multiple single Weyl points, once the effects of the cubic mass $1/M_c$ is included, which is dangerously irrelevant in this case.

A striking experimental consequence of this phase diagram is the AHE due to the Zeeman field, which could originate either from an external magnetic field or as an exchange field due to local moments in the material. The latter is particularly interesting in light of the experimental results on Pr$_2$Ir$_2$O$_7$, which shows a large AHE in a regime where the magnetization $M$ is immeasurably small [@nakatsuji; @machida]. On symmetry grounds, $\sigma_{xy}
\neq 0$ [*implies*]{} $M_z \neq 0$, but evidently $\sigma_{xy}$ is unusually large relative to $M$. This behavior is in fact characteristic of the LAB: since the Hall conductivity has dimensions of inverse length, we expect $\sigma_{xy} \sim H^{1/(z-\eta_{12})} \approx H^{0.51}$. In the situation relevant for Pr$_2$Ir$_2$O$_7$, the 