Critical behaviour of the 1D q-state Potts model with long-range interactions

The critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as $r^{-(1+\sigma )}$ has been studied in the wide range of parameters $0<\sigma \le 1$ and $\frac{1}{16} \le q \le 64$. A transfer matrix has been constructed for a truncated range of interactions for integer and continuous q, and finite range scaling has been applied. Results for the phase diagram and the correlation length critical exponent are presented.