Universal amplitudes ratio at the collapse transition of polymers in two dimensions

First values of the universal ratio of the mean square radius of gyration and the mean square end-to-end distance for 2D linear polymers at their collapse transition are calculated by the scanning simulation method. Two models are considered: (i) self-avoiding walks (SAWs) with nearest-neighbour attractions for which this ratio is found to be 0.179+or-0.003 at the Theta point; (ii) self-intersecting trails at their tricritical point for which the value 0.166+or-0.002 is obtained. This provides yet another indication that these models may belong to different tricritical universality classes. The authors have also computed this ratio for trails at the high temperature limit (with non-interacting intersections) and found 0.141+or-0.001 in excellent agreement with earlier estimates of this ratio for SAWs in their swollen phase.