Abstract
We studied the critical properties of flexible polymers, modelled by self-avoiding random walks, in good solvents and homogeneous environments. By applying the PERM Monte Carlo simulation method, we generated the polymer chains on the square and the simplecubic lattice of the maximal length of N=2000 steps.We enumerated approximately the number of different polymer chain configurations of length N,and analysed its asymptotic behaviour (for large N), determined by the connectivity constant μ and the entropic critical exponent γ. Also, we studied the behaviour of the set of effective critical exponents 휈푁, governing the end-to-end distance of a polymer chain of length N. We have established that in two dimensions 휈푁monotonically increases with N, whereas in three dimensions itmonotonically decreases when Nincreases. Values of 휈푁, obtained for both spatial dimensions have been extrapolated in the range of very long chains.In the end, we discuss and compare our results to those obtained previously for polymers on Euclidean lattices.
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