A Bedini, A L Owczarek, T Prellberg
There has been continued numerical work on the identification of scaling dimensions of an integrable two-dimensional lattice model of polymers via transfer matrix methods. The polymer model is known as the semi-flexible VISAW model and the integrable point is located at a particular set of Boltzmann weights. This point has been argued to describe the collapse phase transition of the polymer. We directly investigate the polymer scaling exponents, related to the scaling dimensions, via Monte Carlo simulations using the PERM algorithm. The polymer model was originally investigated via the exact solution of the O(n) loop model and the polymer exponents, $\nu=12/23\approx 0.522$ and $\gamma=53/46\approx 1.152$, were subsequently found via identification of the scaling dimensions $x_t=1/12$ and $x_h=-5/48$. 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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http://arxiv.org/abs/1211.0252
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