Numerical simulation of a lattice polymer model at its integrable point

We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Bl\"ote and Nienhuis in J. Phys. A. {\bf 22}, 1415 (1989) and it describes polymers with some attraction, providing thus a model for the polymer collapse transition. At a particular set of Boltzmann weights the model is integrable and the exponents $\nu=12/23\approx 0.522$ and $\gamma=53/46\approx 1.152$ have been computed via identification of the scaling dimensions $x_t=1/12$ and $x_h=-5/48$. We directly investigate the polymer scaling exponents via Monte Carlo simulations using the PERM algorithm. By simulating this polymer model for walks up to length 4096 we find $\nu=0.576(6)$ and $\gamma=1.045(5)$, which are clearly different from the predicted values. Our estimate for the exponent $\nu$ is compatible with the known $\theta$-point value of 4/7 and in agreement with very recent numerical evaluation by Foster and Pinettes.