THE ISING-MODEL ON A SAW

Using a renormalization group calculation, we show that the most probable value of the static correlation function of the Ising model on a SAW decays as a stretched exponential (with an exponent equal to the dimension D of the SAW). We prove that the thermal exponent nu(T) equals D-1. On the basis of extensive Monte Carlo simulations we conclude that the spin-spin autocorrelation function also decays as a stretched exponential. We find evidence for a breakdown of dynamical scaling.