  We study a Dirac fermion model with a random vector field, especially paying
attention to a strong disorder regime. Applying the bosonization techniques, we
first derive an equivalent sine-Gordon model, and next average over the random
vector field using the replica trick. The operator product expansion based on
the replica action leads to scaling equations of the coupling constants
(``fugacities'') with nonlinear terms, if we take into account the fusion of
the vertex operators. These equations are converted into a nonlinear diffusion
equation known as the KPP equation. By the use of the asymptotic solution of
the equation, we calculate the density of state, the generalized inverse
participation ratios, and their spatial correlations. We show that results
known so far are all derived in a unified way from the point of view of the
renormalization group. Remarkably, it turns out that the scaling exponent
obtained in this paper reproduces the recent numerical calculations of the
density correlation function. This implies that the freezing transition has
actually revealed itself in such calculations.
