J. Phys. I France
Volume 5, Numéro 5, May 1995
Page(s) 597 - 606
DOI: 10.1051/jp1:1995153
J. Phys. I France 5 (1995) 597-606

Simulations of $\theta$-Polymers in 2 Dimensions

Peter Grassberger and Rainer Hegger

Physics Department, University of Wuppertal, 42097 Wuppertal, Germany

(Received 7 March 1994, revised 7 December 1994, accepted 18 January 1995)

Using a new recursive sampling algorithm, we present simulation results for single 2D chain polymers near and below the $\theta$-point. They involve much longer chains than previous simulations (high statistics for chain lengths up to 2048, a few chains having even 40,000 monomers). Good agreement is found with the exponents derived by Duplantier and Saleur, in contrast to previous Monte Carlo simulations. No indication is found for a two-step collapse, as suggested recently by Orlandini et al ., or for an alternative set of critical indices derived by Warnaar et al. Instead, we find evidence for a surface term in the free energy, as proposed by Owczarek et al.

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