Phase transitions in two-dimensional Z(N) vector models for N > 4

We investigate both analytically and numerically the renormalization group equations in two-dimensional (2D) Z(N) vector models. The position of the critical points of the two phase transitions for N > 4 is established and the critical index. is computed. For N = 7 and 17 the critical points are located by Monte Carlo simulations, and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for N = 5, 7, and 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with N and some other open theoretical problems.