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The phase diagram of the O(n) model, in particular the special case $n=0$, isstudied by means of transfer-matrix calculations on the loop representation ofthe O(n) model. The model is defined on the square lattice; the loops areallowed to collide at the lattice vertices, but not to intersect. The loopmodel contains three variable parameters that determine the loop density ortemperature, the energy of a bend in a loop, and the interaction energy ofcolliding loop segments. A finite-size analysis of the transfer-matrix resultsyields the phase diagram in a special plane of the parameter space. Theseresults confirm the existence of a multicritical point and an Ising-likecritical line in the low-temperature O(n) phase.Comment: LaTeX, 3 eps file

PHASE DIAGRAM OF A LOOP ON THE SQUARE LATTICE