  Random bond Hamiltonians of the $\pi$ flux state on the square lattice are
investigated. It has a special symmetry and all states are paired except the
ones with zero energy. Because of this, there are always zero-modes. The states
near $E=0$ are described by massless Dirac fermions. For the zero-mode, we can
construct a random lattice fermion without a doubling and quite large systems (
up to $801 \times 801$) are treated numerically. We clearly demonstrate that
the zero-mode is given by a critical wave function. Its multifractal behavior
is also compared with the effective field theory.
