Numerical simulation of a lattice polymer model at its integrable point

Abstract

We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Blöte 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.

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References in corpus (3)

• Collapse transition of self-avoiding trails on the square lattice
• Weighting of topologically different interactions in a model of two-dimensional polymer collapse
• Surface critical behaviour of the vertex-interacting self-avoiding walk on the square lattice

Cited by in corpus (4)

• Critical Behaviour of Magnetic Polymers in Two and Three Dimensions
• Grand-canonical solution of semi-flexible self-avoiding trails on the Bethe lattice
• Polymer models with competing collapse interactions on Husimi and Bethe lattices
• Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge