Finite-size scaling analysis on the phase transition of a ferromagnetic polymer chain model

The finite-size scaling analysis method is applied to study the phase transition of a self-avoiding walking polymer chain with spatial nearest-neighbor ferromagnetic Ising interaction on the simple cubic lattice. Assuming the scaling M2(T,n) = n(-2beta/nu)[phi0 + phi1n(1/nu)(T-T(c)) + O(n(2/nu)(T-T(c))2)] with the square magnetization M2 as the order parameter and the chain length n as the size, we estimate the second-order phase-transition temperature T(c) = 1.784 J/k(B) and critical exponents 2beta/nu approximately 0.668 and nu approximately 1.0. The self-diffusion constant and the chain dimensions (R2) and (S2) do not obey such a scaling law.