  Two-dimensional (2D) disordered superconductor (SC) in class D exhibits a
disorder-induced quantum multicritical phenomenon among diffusive thermal metal
(DTM), topological superconductor (TS), and conventional localized (AI) phases.
To characterize the quantum tricritical point where these three phases meet, we
carry out a two-loop renormalization group (RG) analysis for 2D Dirac fermion
with random mass in terms of the $\epsilon$-expansion in the spatial dimension
$d=2-\epsilon$. In 2D ($\epsilon=0$), the random mass is marginally irrelevant
around a clean-limit fixed point of the gapless Dirac fermion, while there
exists an IR unstable fixed point at finite disorder strength that corresponds
to the tricritical point. The critical exponent, dynamical exponent, and
scaling dimension of the (uniform) mass term are evaluated around the
tricritical point by the two-loop RG analysis. Using a mapping between an
effective theory for the 2D random-mass Dirac fermion and the (1+1)-dimensional
Gross-Neveu model, we further deduce the four-loop evaluation of the critical
exponent, and the scaling dimension of the uniform mass around the tricritical
point. Both the two-loop and four-loop results suggest that criticalities of a
AI-DTM transition line as well as TS-DTM transition line are controlled by
other saddle-point fixed point(s) at finite uniform mass.
