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 T_θ. As expected, the critical exponents describing the size of the chain and the partition sum at T=T_θ 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 T_θ−T is not as predicted by mean‐field theory.