  The magnetic field responses of the zero-bias conductance peak (ZBCP) in
tunneling spectra of high $T_{C}$ cuprate junctions are studied theoretically.
Our calculation is based on the lattice Green's function method and takes the
realistic electronic structure of the high $T_{C}$ cuprate into account. In
marked contrast to previous works, it is shown that the critical magnetic field
strength $H_{C}$ exists for the splittings of the ZBCP's to be discernible.
$H_{C}$ is almost proportional to the product of the magnitude of pair
potential, transmissivity of the junction, and the inverse of the Fermi
velocity parallel to the interface (1/$v_{Fy}$). The calculated $H_{C}$'s for
the hole-doped superconductors are higher than those for electron-doped ones
because of relatively large magnitude of pair potential and the small magnitude
of $v_{Fy}$ originating from peculiar shape of the Fermi surface.
