  The three-dimensional real scalar model, in which the $Z_2$ symmetry
spontaneously breaks, is renormalized in a nonperturbative manner based on the
Tamm-Dancoff truncation of the Fock space. A critical line is calculated by
diagonalizing the Hamiltonian regularized with basis functions. The marginal
($\phi^6$) coupling dependence of the critical line is weak. In the broken
phase the canonical Hamiltonian is tachyonic, so the field is shifted as
$\phi(x)\to\varphi(x)+v$. The shifted value $v$ is determined as a function of
running mass and coupling so that the mass of the ground state vanishes.
