Effective mass and tricritical point for lattice fermions localized by a random mass

This is a numerical study of quasiparticle localization in symmetry class \textit{BD} (realized, for example, in chiral \textit{p}-wave superconductors), by means of a staggered-fermion lattice model for two-dimensional Dirac fermions with a random mass. For sufficiently weak disorder, the system size dependence of the average (thermal) conductivity $\sigma$ is well described by an effective mass $M_{\rm eff}$, dependent on the first two moments of the random mass $M(\bm{r})$. The effective mass vanishes linearly when the average mass $\bar{M}\to 0$, reproducing the known insulator-insulator phase boundary with a scale invariant dimensionless conductivity $\sigma_{c}=1/\pi$ and critical exponent $\nu=1$. For strong disorder a transition to a metallic phase appears, with larger $\sigma_{c}$ but the same $\nu$. The intersection of the metal-insulator and insulator-insulator phase boundaries is identified as a \textit{repulsive} tricritical point.