Simulations of three-dimensional θ polymers

Using a new recursive sampling algorithm, we present simulation results for single three-dimensional chain polymers at and below the θ point. These simulations extend far into hitherto inaccessible regions as concerns chain length (up to N=5000 for free chains, up to N=300 000 for chains in a finite volume with periodic boundary conditions) and temperature. They show that the collapse is very sudden for large N, leading, e.g., to a nonmonotonic dependence of the end-to-end distance on N for fixed temperatures slightly below Tθ. As expected, the critical exponents describing the size of the chain and the partition sum at T=Tθ are of mean-field type. But the logarithmic corrections to this mean-field behavior are very different from those predicted by field theoretic methods. Also, the critical exponent which describes how the monomer density deep inside a collapsed chain increases with Tθ−T is not as predicted by mean-field theory.