Using the scanning simulation method, we study self-attracting trails (with energy ɛ per intersection) terminally attached to an im- penetrable linear boundary on a square lattice at their tricrital collapse transition. Our results for the exponents of the partition functions are ${\gamma }_1$=0.634±0.025 (one end attached to the surface) and ${\gamma }_{11}$=-0.44±0.02 (both ends attached). These values (with 95% significance limits) are within the error bars of the numerical estimates of Seno and Stella [Europhys. Lett. 7, 605 (1989)] for self-avoiding walks (SAW’s) at the FTHETA-point on the same lattice. Our results, however, differ significantly from the exact values derived by Duplantier and Saleur for SAW’s on a dilute hexagonal lattice at the FTHETA’ point. The collapse temperature $T_t$ and the tricritical growth parameter μ are very close to their analytic bounds -ɛ/$k_B$$T_t$=ln3 and μ=3.

• Received 12 May 1989

DOI:https://doi.org/10.1103/PhysRevA.40.2879