  The phase diagram of the O(n) model, in particular the special case $n=0$, is
studied by means of transfer-matrix calculations on the loop representation of
the O(n) model. The model is defined on the square lattice; the loops are
allowed to collide at the lattice vertices, but not to intersect. The loop
model contains three variable parameters that determine the loop density or
temperature, the energy of a bend in a loop, and the interaction energy of
colliding loop segments. A finite-size analysis of the transfer-matrix results
yields the phase diagram in a special plane of the parameter space. These
results confirm the existence of a multicritical point and an Ising-like
critical line in the low-temperature O(n) phase.
