DISTRIBUTION OF THE ORDER-PARAMETER OF THE COIL-GLOBULE TRANSITION

We investigate the probability distribution P-N(r) of the radius of gy ration r of a polymer chain of size N with excluded-volume interaction s at infinite temperature. This function shows the geometric contribut ion to the tricritical coil-globule transition of self-avoiding walks; it indicates that the relevant order parameter t of the transition is a power of the density rho = Nr(-d). The theoretical form of die dist ribution P-N(t) of this order parameter is deduced from scaling argume nts, and supported by numerical simulations. Intending to probe the co ntribution of the different subsets of conformations, namely, globule, coil and stretch, we supplement P-N(t) with a formal Boltzmann factor ; this model undergoes a tricritical coil-globule transition which is solved exactly. We show a nontrivial finite-size scaling for P-N(t) an d analyze its convergence toward the thermodynamic limit. Due to the p resence in P-N(t) of a diverging factor t(c) with c < - 1, this conver gence happens to be tragically slow. As a result, the scaling behavior observed in numerical. simulations is qualitatively different from it s thermodynamic limit, and we relate the critical exponents of the geo metric transition in the thermodynamic limit and the effective exponen ts observed at finite size.