Numerical simulation of a lattice polymer model at its integrable point

TL;DR

This paper uses Monte Carlo simulations to study a lattice polymer model at its integrable point, revealing that the actual scaling exponents differ from the theoretical predictions, and providing new numerical estimates.

Contribution

The study provides the first direct numerical investigation of the polymer scaling exponents at the integrable point, challenging previous theoretical predictions.

Findings

Measured exponents: ν=0.576(6), γ=1.045(5)

Results differ from theoretical predictions

Estimated ν aligns with the θ-point value of 4/7

Abstract

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.